SSC CGL 2023 PYQ — Question 73

The correct answer is option 1 i.e.  10$\sqrt{6}$ .

The ratio of the length of each equal side and the third side of an isosceles triangle is 3 : 5.

If the area of the triangle is 30$\sqrt{11}$ cm²,

Area of isosceles triangle = $\frac{b}{2}\sqrt{a^2-\frac{b^2}{4}}$

a = 3x, b = 5x

⇒ $\frac{5x}{2}\sqrt{(3x)^2-\frac{(5x)^2}{4}}$ =  30$\sqrt{11}$ 

⇒ $\frac{5x}{2}\sqrt{\frac{11x^2}{4}}$ =  30$\sqrt{11}$ 

⇒ $\frac{5x^2}{4}\sqrt{11}$ =  30$\sqrt{11}$ 

⇒ x = 2√6

so, the third side = 5x = 10√6