If Δ ABC ~ Δ QRP; area of Δ ABC : area of Δ PQR = 9 : 4; AB = 18 cm and BC = 15 cm, then find the length of PR.

Question

Question

This question was previously asked in

SSC CHSL Exam 2024 Tier-I Official Paper (Held On: 02 Jul, 2024 Shift 3)

Answer 1

Given:

Δ ABC ~ Δ QRP

Area of Δ ABC : Area of Δ PQR = 9 : 4

AB = 18 cm

BC = 15 cm

Formula Used:

Ratio of the areas of two similar triangles = (Ratio of the corresponding sides)²

Calculation:

F1 SSC Priya 20 8 24 D1

Let the ratio of the corresponding sides of Δ ABC and Δ QRP be k.

Then, \(k^2 = \frac{9}{4}\)

⇒ \(k = \sqrt{\frac{9}{4}}\)

⇒ \( k = \frac{3}{2}\)

Since Δ ABC ~ Δ QRP, the corresponding sides are proportional.

We need to find the length of PR which corresponds to BC.

Let PR = x cm.

Then, \(\frac{BC}{PR}\) = \( \frac{3}{2}\)

⇒ \(\frac{15}{x} = \frac{3}{2}\)

⇒ 15 × 2 = 3 × x

⇒ 30 = 3x

⇒ x = \(\frac{30}{3}\)

⇒ x = 10 cm

The length of PR is 10 cm.

Download Solution PDF