SSC CHSL 2023 PYQ — Question 66

The correct answer is option 1 i.e. $10 \sqrt2 \ m^2$.

Let the third side be x

Perimeter = sum of sides

⇒ 20 = 5 + 6 + x

⇒ x = 20 - 11

⇒ x = 9 m

Heron's formulae

A = $\sqrt{s(s-a)(s-b)(s-c)}$

s = (a + b + c)/2 = (5 + 6 + 9)/2 = 20/2 = 10

So,

⇒ A = $\sqrt{10(10-5)(10-6)(10-9)}$

⇒ A = $\sqrt{10\times 5\times 4\times1}$

⇒ A = 10$\sqrt2$ m²