Equilateral Triangle

Algebra Level 3

One side of an equilateral triangle is 24cm.The mid points of its sides are joined to form another triangle whose mid points are in turn joined to form still another triangle.This process continues indefinitely.Find the sum of the perimeters of all the triangles in cm.

The answer is 144.

1 solution

Akshat Sharda
Nov 2, 2015

$\text{Just a Infinite G.P.}=72+\frac{72}{2^{1}}+\frac{72}{2^{2}}+\frac{72}{2^{3}}+\ldots \infty=\frac{72}{1-\frac{1}{2}}=\boxed{144}$

Equilateral Triangle

The answer is 144.

1 solution

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