SSC GD 2023 PYQ — Question 53

The correct answer is Option 2 i.e. 3√7.

Let a, b, and c be the sides of the triangle

a = b = x and c = 1.5x

We know that, 

Perimeter = Sum of all sides

14 = x + x + 1.5x

14 = 2x + 1.5x

14 = 3.5x

x = 4

So, a = b = 4 and c = 6

By Heron's Formulae

s = (a + b + c)/2 where s = semi-perimeter

s = (4 + 4 + 6)/2 = 14/2 = 7

Area = $\sqrt{s(s-a)(s -b)(s-c)}$

Area = $\sqrt{7(7-4)(7 -4)(7-6)}$

Area = $\sqrt{7\times3\times3\times1}$

The area of the triangle = $3\sqrt{7}$