SSC CHSL 2024 PYQ — Question 57

The correct answer is option 1 i.e. $1 : \sqrt{2}-1$.

We know,

The ratio of the area of similar triangle = (Ratio of corresponding sides)²

Now,

ST || QR and ST divide triangle PQR into two parts of equal areas, area of triangle PST is half of the area of triangle PQR

Let the ratio of the areas be 1 : 2

The ratio of their respective sides, PS : PQ = 1 : √2

⇒ PQ = PS + QS

Let the value of PS and PQ be x and √2x

⇒ PQ = x + QS

⇒ PS/PQ = 1/√2

⇒ x/(x + QS) = 1/√2

⇒ √2x = x + QS

⇒ QS = (√2 - 1)x

Hence, the required ratio of PS : QS = x : (√2 - 1)x

⇒ 1 : (√2 - 1)