One side of an equilateral triangle is 24 cm. The mid-points of its sides are joined to form another triangle whose mid-points -Maths 9th

One side of an equilateral triangle is 24 cm. The mid-points of its sides are joined to form another triangle whose mid-points -Maths 9th
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Perimeter of the largest (outermost) equilateral triangle = 3 × 24 = 72 cm. Now, the perimeter of the triangle formed by joining the midpoints of a given triangle will be half the perimeter of the original triangle. ∴ Required sum = 72 + 36 + 18 + ............. upto infinite terms This is an infinite GP, where first term a = 72 and common ratio r = \(rac{1}{2}.\)∴ Required sum = \(rac{a}{1-r}\) = \(rac{72}{1-rac{1}{2}}\) = \(rac{72}{rac{1}{2}}\) = 72 x 2 = 144 cm.
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