CAT 2017 Slot 1 QA Question 1: From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is $s$. Then the area of the triangle is

Question

From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is $s$. Then the area of the triangle is

Accepted Answer

In an equilateral triangle, the sum of perpendicular distances from any interior point to the three sides is equal to the altitude of the triangle.

$h = s$
$h = \dfrac{\sqrt{3}}{2} 	imes a$
$s = \dfrac{\sqrt{3}}{2} 	imes a$
$a = \dfrac{2s}{\sqrt{3}}$

Area of an equilateral triangle with side $a$

From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is sss. Then the area of the triangle is

From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is $s$ . Then the area of the triangle is