SSC CHSL 2024 PYQ — Question 61

The correct answer is Option 4 i.e. $25\over{\sqrt2}$.

The ratio of the sides of △ABC is 3 : 4 : 5 = 3x : 4x : 5x, and

The smallest side is 15 unit

So, 3x = 15

⇒ x = 5

So, the sides of △ABC = 3x, 4x, 5x = 15, 20, 25 respectively

We know that,

Area of △DEF/Area of △ABC = (k/1)²

The area of △DEF is half the area of △ABC

⇒ 1/2 = k²

⇒ k = $1\over \sqrt2$

The largest side of △ABC is 25 units

So,

The longest side of △DEF = 25k = 25 × $1\over \sqrt2$ = $25\over{\sqrt2}$ units