SSC CGL 2024 PYQ — Question 65

The correct answer is Option 3 i.e. 10$\sqrt{2}$.

In a right-angled isosceles triangle, the two legs are equal in length

Let the length of each leg be x

We know that,

Area of the triangle = 1/2 × base × height

So,

⇒ 50 = 1/2 × x × x

⇒ 50 = 1/2 × x²

⇒ 100 = x²

⇒ x = 10

In a right-angled isosceles triangle, the hypotenuse h is related to the legs by the Pythagorean theorem

⇒ h = $\sqrt{x^2+x^2}$

⇒ h = $\sqrt{2x^2}$

put x = 10

⇒ h = $\sqrt{2\times10^2}$

⇒ h = $\sqrt{200}$

⇒ h = 10$\sqrt2$

Thus, the hypotenuse is 10$\sqrt2$ units