Find the area of a triangle whose sides are 4.5 cm and 10 cm and perimeter 10.5 cm. -Maths 9th

Find the area of a triangle whose sides are 4.5 cm and 10 cm and perimeter 10.5 cm. -Maths 9th
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Step-by-step explanation: ◾As we have given the two sides of triangle, let the three sides of triangle are (a) , (b), (c) . ◾And perimeter of given triangle is 10.5 cm ◾were, let us assume the sides are, side a = 4.5 cm side b = 10 cm side c = ? we know, ◾perimeter of triangle = sum of all sides of triangle 10.5 = side a + side b + side c 10.5 = 4.5 + 10 + side c 10.5 = 14.5 + side c 10.5 - 14.5 = side c side c = 4 cm [side be never in negative ] therefor, ◾Now, we can use Hero's formula to find the area of triangle when sides of triangle are given. ◾Hero's formula Hero's formula for area of triangle = √[ s ( s - a ) ( s - b) (s - c) ] ◾For using this formula, we need to find the s (semiperimeter) S = [side a + side b + side c ] / 2 = [ 4.5 + 10 + 4 ] / 2 = 9.25 cm Therefor , ◾Area of triangle abc = √[ s ( s - a ) ( s - b) (s - c) ] = √[ 9.25 ( 9.25 - 4.5 ) ( 9.25 - 10 ) (9.25 - 4 ) ] = √ [ 9.25 (( 4.75 ) ( -0.75 ) ( 5.25 ))] =√ [( (9.25 ) (-3.5625) ( 5.25 )) = √[ ((48.5625) ( (-3.5625)) ] = √ [ 173 ( approximately) ] = 13.15 ( approximately) ◾In the above, (-3.5625)) we taken as a (3.5625 ) because area is never as an imaginary . ◾here, we took a value (13.15) as an approx, up-to two decimals . ◾So, the area of a triangle whose sides are 4.5 cm and 10 cm and perimeter 10.5 [Area ]=
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If the sides of a triangle are 3 cm, 4 cm and 5 cm, then what is the radius of the circum-circle? -Maths 9th

Description : If the sides of a triangle are 3 cm, 4 cm and 5 cm, then what is the radius of the circum-circle? -Maths 9th

Last Answer : Semi-perimeter of triangle (s) = \(rac{3+4+5}{2}\)cm = 6 cm∴ Area of triangle A = \(\sqrt{s(s-a)(s-b)(s-c)}\) = \(\sqrt{6 imes3 imes2 imes1}\) cm2 = 6 cm2∴ Radius of circum-circle = \(rac{abc}{4( ext{Area of}\,\Delta)}\) = \(rac{3+4+5}{4 imes60}\) cm = 2.5 cm

If the lengths of a sides of a triangle are in the ratio 4 : 5 : 6 and the in-radius of the triangle is 3 cm, -Maths 9th

Description : If the lengths of a sides of a triangle are in the ratio 4 : 5 : 6 and the in-radius of the triangle is 3 cm, -Maths 9th

Last Answer : (b) 7.5 cm.Area of a triangle = \(rac{1}{2}\)x base x height= In-radius x semi-perimeter of the Δ \(\big[ ext{Using r =}rac{\Delta}{s}\big]\)Let the sides of triangle be 4x, 5x and 6x respectively. Given: In-radius = 3 ... x \(rac{15x}{2}\) = \(rac{6x}{2}\) x h ⇒ h = \(rac{45}{6}\) = 7.5 cm.

Find the area of a triangle having perimeter 32cm. One side of its side is equal to 11cm and difference of the other two is 5cm. -Maths 9th

Description : Find the area of a triangle having perimeter 32cm. One side of its side is equal to 11cm and difference of the other two is 5cm. -Maths 9th

Last Answer : Solutions :- We have, Perimeter of triangle = 32 cm One of its side = 11 cm Let the second side be x And third side be x + 5 Perimeter of triangle = sum of three sides A/q => 11 + x + x + 5 ... 13 cm Now, By using heron's formula, Find the area of a triangle :- Answer : Area of triangle = 43.81 cm²

If the perimeter of an equilateral triangle is 24cm, then find the area of the triangle -Maths 9th

Description : If the perimeter of an equilateral triangle is 24cm, then find the area of the triangle -Maths 9th

Last Answer : Perimeter of equilateral triangle = 24cm ( there are three equal sides in an e quilateral triangle ) Each side = 24 / 3 = 8cm Area of an equilateral triangle = root 3 / 4 s square = root 3 / 4 × 8 square = root 3 / 4 x 64 = root 3 × 16 = 16 root 3