If a right triangle has a hypotenuse of 12 cm and one leg that measures 9 cm find the length of the other leg.?

1 Answer

Answer :

Using Pythagoras' theorem for a right angle triangle the otherleg is 3 times the square root of 7

Related questions

Description : The base of a right-angled triangle measures 4 cm and its hypotenuse measures 5 cm. Find the area of the triangle. -Maths 9th

Last Answer : In right-angled triangle ABC AB2 + BC2 = AC2 (By Pythagoras Theorem) ⇒ AB2 + 42 = 52 ⇒ AB2 = 25 – 16 = 9 5 cm ⇒ AB = 3 cm ∴ Area of △ABC = 1/2 BC x AB = 1/2 x 4 x 3 = 6cm2

Description : Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm. -Maths 9th

Last Answer : Steps of Construction (i) Draw BC = 12 cm. (ii) Construct ÐCBY = 90°. (iii) From ray BY, cut-off line segment BD = 18 cm. (iv) Join CD. (v) Draw the perpendicular bisector of CD intersecting BD at A. (vi ... = AC Now, BD = BA + AD ⇒ BD = AB + AC Hence, △ABC is the required triangle.

Description : If the length of hypotenuse of a right angled triangle is 5 cm and its area is 6 sq cm, then what are the lengths of the remaining sides? -Maths 9th

Last Answer : Let one of the remaining sides be x cm.Then, other side = \(\sqrt{5^2-x^2}\) cm∴ Area = \(rac{1}{2} imes{x} imes\sqrt{25-x^2}\) = 6⇒ \(x\sqrt{25-x^2}\) = 12 ⇒ x2(25 - x2) = 144⇒ 25x2 - x4 = 144 ⇒ x4 - 25x2 ... (x2 - 16) (x2 - 9) = 0 ⇒ x2 = 16 or x2 = 9 ⇒ x = 4 or 3∴ The two sides are 4 cm and 3 cm.

Description : what- Fill in the blanks to the Hypotenuse- Leg Congruence Theorem.If the hypotenuse and leg of one right triangle are _____ to the _____ of another right triangle, then the triangles are congruent?

Last Answer : congruent; hypotenuse and a leg

Description : A right triangle when one side is 3.5 cm and sum of other sides and the hypotenuse is 5.5 cm. -Maths 9th

Last Answer : Let given right triangle be ABC. Then, given BC = 3.5 cm, ∠B = 90° and sum of other side and hypotenuse i.e., AB + AC = 5.5 cm To construct ΔABC use the following steps 1.Draw the base BC = 3.5 cm 2.Make ... AB = BD - AD = BD - AC [from Eq. (i)] => BD = AB + AC Thus, our construction is justified.

Description : A right triangle when one side is 3.5 cm and sum of other sides and the hypotenuse is 5.5 cm. -Maths 9th

Last Answer : Let given right triangle be ABC. Then, given BC = 3.5 cm, ∠B = 90° and sum of other side and hypotenuse i.e., AB + AC = 5.5 cm To construct ΔABC use the following steps 1.Draw the base BC = 3.5 cm 2.Make ... AB = BD - AD = BD - AC [from Eq. (i)] => BD = AB + AC Thus, our construction is justified.

Description : What median of an isosceles triangle is the same segment in the triangle as the leg bisector hypotenuse altitude?

Last Answer : It is the median which divides the side which is not one of theequal sides.

Description : The perimeter of a right triangle is 30 cm. If its hypotenuse is 13 cm, then what are two sides? -Maths 9th

Last Answer : The other two sides of the triangle are 12 cm and 5 cm Explanation: Let the other two sides of triangle be x and y It's hypotenuse is 13 cm Perimeter of triangle = Sum of all sides ... When y = 12 x=17-y = 17-12 =5 So, the other two sides of the triangle are 12 cm and 5 cm

Description : ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that (i) D is the mid-point of AC (ii) MD ⊥ AC (iii) CM = MA = ½ AB -Maths 9th

Last Answer : Solution: (i) In ΔACB, M is the midpoint of AB and MD || BC , D is the midpoint of AC (Converse of mid point theorem) (ii) ∠ACB = ∠ADM (Corresponding angles) also, ∠ACB = 90° , ∠ADM = 90° and MD ⊥ AC (iii ... SAS congruency] AM = CM [CPCT] also, AM = ½ AB (M is midpoint of AB) Hence, CM = MA = ½ AB

Description : A right triangle has one side that is 7 cm longer than its shortest side. The triangle’s hypotenuse is 8 cm longer than the shortest side. What are the dimensions of the triangle?

Last Answer : extra 6 dimensions of 10 dimensional spacetime

Description : Is it possible for a right angled triangle with sides 3 and 4 units long to have a hypotenuse 6 units in length?

Last Answer : answer:I'm not quite getting you. It isn't actually a triangle when the hypotenuse has these indentations, right? The hypotenuse isn't a straight line as you describe it. If the other sides are 3 ... and 5.00001, you don't have a straight line. Unless I'm misunderstanding what you're suggesting.

Description : An isosceles right triangle has area 8 cm2. The length of its hypotenuse is -Maths 9th

Last Answer : (a) Given, area of an isosceles right triangle = 8 cm2 Area of an isosceles triangle = 1/2 (Base x Height) ⇒ 8 = 1/2 (Base x Base) [∴ base = height, as triangle is an ... √32 cm [taking positive square root because length is always positive] Hence, the length of its hypotenuse is √32 cm.

Description : An isosceles right triangle has area 8 cm2. The length of its hypotenuse is -Maths 9th

Last Answer : This answer was deleted by our moderators...

Description : An isosceles right triangle has area 8 cm2 . Find the length of its hypotenuse. -Maths 9th

Last Answer : Area = 1/2a2 ⇒ 1/2a2 = 8 ⇒ a2 = 16 cm ⇒ a = 4 cm Hypotenuse = √2a = √2.4 = 4√2 cm.

Description : Let a, b, c be the lengths of the sides of a right angled triangle, the hypotenuse having the length c, then a + b is -Maths 9th

Last Answer : answer:

Description : Prove that the points (2, –2), (–2, 1) and (5, 2) are the vertices of a right angled triangle. Also find the length of the hypotenuse -Maths 9th

Last Answer : Let the co-ordinates of any point on the x-axis be (x, 0). Then distance between (x, 0) and (– 4, 8) is 10 units.⇒ \(\sqrt{(x+4)^2+(0-8)^2}\) = 10 ⇒ x2 + 8x + 16 + 64 = 100 ⇒ x2 + 8x – 20 = 0 ⇒ (x + 10) (x – 2) = 0 ⇒ x = –10 or 2 ∴ The required points are (– 10, 0) and (2, 0).

Description : If a right triangle has legs of length 6 and 8 then we know the length of the hypotenuse is the square root of 6 plus 8 which equals 10?

Last Answer : Using Pythagoras theorem: 6^2 + 8^2 = 100 and its square root is10 which is the length of the hypotenuse

Description : What is the length of the hypotenuse of the triangle?

Last Answer : Consider triangle QRS. The legs each have a length of ten units

Description : In an isoceles triangle what is the length of the hypotenuse if 2 legs are 30?

Last Answer : If it is a right angle isosceles triangle then by usingPythagoras' theorem its hypotenuse is 30 times the square root of2

Description : How do you determine the length of the 3rd leg in a right triangle if you have the length of the other two legs?

Last Answer : A right triangle only has two legs, the third side is called thehypotenuse . The square of the length of the hypotenuse is equal tothe sum of the squares of the two legs. The square root of ... the square of the hypotenuse and the square of oneleg is equal to the length of the other leg.

Description : In a right angle triangle, prove that the hypotenuse is the longest side. -Maths 9th

Last Answer : The sum of angles of a triangle is180° If one aangke is of 90° then the sum of two angles is 90° It means that the angle forming 90° is biggest angle We know , Angle opposite to the longest side is largest. It means hypotenuse is the biggest side of right angled triangle

Description : ABC is a triangle right-angled at C. A line through the mid-point M of hypotenuse AB parallel to BC intersects AC ad D. -Maths 9th

Last Answer : Given: A △ABC , right - angled at C. A line through the mid - point M of hypotenuse AB parallel to BC intersects AC at D. To Prove: (i) D is the mid - point of AC (ii) MD | AC (iii) CM = MA = 1 / 2 ... congruence axiom] ⇒ AM = CM Also, M is the mid - point of AB [given] ⇒ CM = MA = 1 / 2 = AB.

Description : In a right angle triangle, prove that the hypotenuse is the longest side. -Maths 9th

Last Answer : The sum of angles of a triangle is180° If one aangke is of 90° then the sum of two angles is 90° It means that the angle forming 90° is biggest angle We know , Angle opposite to the longest side is largest. It means hypotenuse is the biggest side of right angled triangle

Description : ABC is a triangle right-angled at C. A line through the mid-point M of hypotenuse AB parallel to BC intersects AC ad D. -Maths 9th

Last Answer : Given: A △ABC , right - angled at C. A line through the mid - point M of hypotenuse AB parallel to BC intersects AC at D. To Prove: (i) D is the mid - point of AC (ii) MD | AC (iii) CM = MA = 1 / 2 ... congruence axiom] ⇒ AM = CM Also, M is the mid - point of AB [given] ⇒ CM = MA = 1 / 2 = AB.

Description : ABC is a triangle right-angled at C. A line through the mid-point of hypotenuse AB and parallel to BC intersects AC at D. Show that -Maths 9th

Last Answer : Solution :-

Description : In a right-angled triangle ABC, D is the foot of the perpendicular from B on the hypotenuse AC -Maths 9th

Last Answer : Area of ΔABC = \(rac{1}{2}\) x 3 x 4 cm2 = 6 cm2. Also, AC = \(\sqrt{3^2+4^2}\) = 5 cm.∴ Area of ΔABC = \(rac{1}{2}\) x BD x AC ⇒ 6 = \(rac{1}{2}\) BD x 5 ⇒ BD = \(rac{12}{5}\) cm.Now in ΔABD, AD = \(\ ... \(rac{1}{2}\)x AD x BD = \(rac{1}{2}\) x \(rac{9}{5}\) x \(rac{12}{5}\) = \(rac{54}{25}\) cm2.

Description : The hypotenuse of an isosceles right-angled triangle is q. If we describe equilateral triangles (outwards) on all its three sides, -Maths 9th

Last Answer : (b) \(rac{q^2}{4}\) (2√3 + 1).AC = q, ∠ABC = 90º ⇒ q = \(\sqrt{AB^2+BC^2}\)⇒ q = \(\sqrt{2x^2}\)⇒ q2 = 2x2 ⇒ \(x\) = \(rac{q}{\sqrt2}\)∴ Area of the re-entrant hexagon = Sum of areas of (ΔABC + ΔADC ... (rac{\sqrt3}{4}\)q2 + \(rac{\sqrt3}{8}\)q2 + \(rac{\sqrt3q^2}{8}\) = \(rac{q^2}{4}\) (2√3 + 1).

Description : A piece of paper is in the shape of a right-angled triangle and is cut along a line that is parallel to the hypotenuse, leaving a smaller triangle. -Maths 9th

Last Answer : (d) 14.365Given, ST || RQ∴ \(rac{ ext{Area of ΔSPT}}{ ext{Area of ΔRPQ}}\) = \(rac{ST^2}{RQ^2}\)Also, given ST = \(\bigg(1-rac{35}{100}\bigg)RQ\) = (0.65) RQ∴ \(rac{ST}{RQ}\) = 0.65 ⇒ \(\bigg(rac ... ΔRPQ}}\) = 0.4225 ⇒ \(rac{ ext{Area of ΔSPT}}{{34}}\) = 0.4225⇒ Area of ΔSPT = 0.4225 x 34 = 14.365

Description : Let ABC be a right angled triangle with AC as its hypotenuse. Then, -Maths 9th

Last Answer : answer:

Description : Is this statement true or falseThe circumcenter of a right triangle always lies on the hypotenuse?

Last Answer : 1

Description : In a right triangle the hypotenuse is always shortest of the three sides?

Last Answer : False because the hypotenuse is always the longest side which isopposite the biggest angle of 90 degrees

Description : In a right triangle the hypotenuse is always the shortest of the three sides.?

Last Answer : No, it is not the shortest side. The hypotenuse is the longest side. Also, it's always opposite the right angle.

Description : How do you find the altitude of the hypotenuse in a right triangle?

Last Answer : By using Pythagoras' theorem: hypotenuse^2 minus base^2 =altitude^2

Description : The sides of a triangle are in the ratio of 1/2:1/3:1/4. If its perimeter is 52 cm, the length of the smallest side is : (A) 9 cm (B) 10 cm (C) 11 cm (D) 12 cm

Last Answer : (D) 12 cm Answer: D Explanation: Sides of a triangle are in the ratio of a:b:c = 1/2:1/3:1/4 = 12 /2 : 12 /3 : 12 /4 = 6:4:3 Let the lengths of three sides of the triangle be 6x, 4x, 3x Perimeter of the ... ⇒ 52 cm = 6x + 4x + 3x x = 52/13 = 4 cm length of the smallest side = 3x = 3 x 4 = 12 cm

Description : a square is inscribed in an isosceles triangle so that the square and the triangle have one angle common. show that the vertex of the square opposite the vertex of the common angle bisect the hypotenuse. -Maths 9th

Last Answer : This answer was deleted by our moderators...

Description : Find the area of an isosceles triangle, whose equal sides are of length 15 cm each and third side is 12 cm. -Maths 9th

Last Answer : We have, Three sides13cm,13cm and 20cm. By using Heron's formula We need to get the semi-perimeter s= 2 a+b+c​ = 2 13+13+20​ = 2 46​ =23 Now, put the heron's formula, s= s(s−a)(s−b)(s−c)​ = 23(23−13)(23−13)(23−20)​ = 23×10×10×3​ =10 23×3​ =83.07cm 2

Description : What type of triangle has side measures of 6 cm 7 cm and W cm and one angle with a measure of 120?

Last Answer : It is an obtuse angled triangle.

Description : What type of triangle has side measures of 6 cm 7 cm and W cm and one angle with a measure of 120?

Last Answer : It is an obtuse angled triangle.

Description : The lengths of three medians of a triangle are 9 cm, 12 cm and 15 cm. The area (in sq. cm) of this triangle is -Maths 9th

Last Answer : (b) 72 cm2Here sm = \(rac{9+12+15}{2}\) = 18 cm, where lengths of medians are m1 = 9 cm, m2 = 12 cm, m3 = 15 cm.∴ Area of triangle = \(rac{4}{3}\sqrt{18(18-9)(18-12)(18-15)}\) cm2= \(rac{4}{3}\sqrt{18 imes9 imes6 imes3}\) cm2 = \(rac{4}{3}\) x 9 x 6 cm2 = 72 cm2.

Description : Each side of an equilateral triand 12 is \( 24 cm \) the mid - point of its sides are joined to form another tranpla this brress is doins centinuously infinite46. The perimeter of 7 th triangle is \( ( \) in \( cm ) \)a) \( \ ... of the 5th triangle is (in \( cm \) )a) 6b) \( 1.5 \)c) \( 0.75 \)d) 3

Last Answer : Each side of an equilateral triand 12 is \( 24 cm \) the mid - point of its sides are joined to form another tranpla ... ( 1.5 \) c) \( 0.75 \) d) 3

Description : If theHypotenuse of a right triangle is 6cm and one leg is 3cm?

Last Answer : Using Pythagoras' theorem for a right angle triangle then theother leg works out as 3 times the square root of 3 or about 5.196cm rounded to three decimal places

Description : If theHypotenuse of a right triangle is 6cm and one leg is 3cm?

Last Answer : Using Pythagoras' theorem for a right angle triangle then theother leg works out as 3 times the square root of 3 or about 5.196cm rounded to three decimal places

Description : Sides of triangles are (i) 3 cm, 4 cm, 6 cm. (ii) 4 cm, 5 cm, 6 cm. (iii) 7 cm, 24 cm, 25 cm (iv) 5 cm, 12 cm, 14 cm. Which of these is right triangle?(a) (i) (b) (ii) (c) (iii) (d) (iv)

Last Answer : (c) (iii)

Description : What is length of hypotenuse if 2 legs are 30 inches?

Last Answer : If it is a right angle triangle then using Pythagoras; theoremits hypotenuse is 30 times the square root of 2 in inches which isabout 42.426 inches rounded to 3 decimal places.

Description : ABC and ADC are two right triangles with common hypotenuse AC. Prove that angle CAD = angle CAB -Maths 9th

Last Answer : Given, AC is the common hypotenuse. ∠B = ∠D = 90°. To prove, ∠CAD = ∠CBD Proof: Since, ∠ABC and ∠ADC are 90°. These angles are in the semi circle. Thus, both the triangles are lying in the semi ... D are concyclic. Thus, CD is the chord. ⇒ ∠CAD = ∠CBD (Angles in the same segment of the circle)

Description : On a common hypotenuse AB, two right angled triangles, ACB and ADB are situated on opposite sides. -Maths 9th

Last Answer : According to question ∠BAC = ∠BDC.

Description : ABC and ADC are two right triangles with common hypotenuse AC. Prove that angle CAD = angle CAB -Maths 9th

Last Answer : Given, AC is the common hypotenuse. ∠B = ∠D = 90°. To prove, ∠CAD = ∠CBD Proof: Since, ∠ABC and ∠ADC are 90°. These angles are in the semi circle. Thus, both the triangles are lying in the semi ... D are concyclic. Thus, CD is the chord. ⇒ ∠CAD = ∠CBD (Angles in the same segment of the circle)

Description : On a common hypotenuse AB, two right angled triangles, ACB and ADB are situated on opposite sides. -Maths 9th

Last Answer : According to question ∠BAC = ∠BDC.

Description : In a rhombus if d1 = 16 cm, d2 = 12 cm, then the length of the side of the rhombus is (a) 8 cm (b) 9 cm (c) 10 cm (d) 12 cm

Last Answer : (c) 10 cm

Description : A cuboid shaped wooden block has 6 cm length, 4 cm breadth and 1 cm height. 7. Two faces measuring 4 cm x 1 cm are coloured in black. 8. Two faces measuring 6 cm x 1 cm are coloured in red. 9. Two faces measuring ... 1 cm(from 4 cm side). How many small cubes will be formed? (a)6 (b)12 (c)16 (d)24

Last Answer : Answer key : (d)