CAT 2018 Slot 1 QA Question 21: Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides o

Question

Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides o

Accepted Answer

The area of the first equilateral triangle is
$\dfrac{\sqrt{3}}{4} 	imes 24^{2} = 144\sqrt{3}$
Each new triangle has side half of the previous triangle, so its area is one-fourth of the previous area.
The required sum is an infinite GP.
Sum $=\{144\sqrt{3}}{1 - \dfrac{1}{4}}$
$=\dfrac{144\sqrt{3} \