Question

If the area of ΔABC is 25 cm² and the area of ΔPQR is 49 cm² and the length of the side QR is 3 cm. Find the length of the side BC if ΔABC ~ ΔPQR.
1. 15/7 cm
2. 7/5 cm
3. 21/5 cm
4. 5/21 cm

Answer 1

Correct Answer - Option 1 : 15/7 cm

Given:

ΔABC ~ ΔPQR

Area of ΔABC = 25 cm²

Area of ΔPQR = 49 cm²

Length of QR = 3 cm

Concept used:

The ratio of the area of any two similar triangles is equal to the ratio of the squares of their corresponding sides.

 If ΔABC ~ ΔPQR,

ar(ΔABC)/ar(ΔPQR) = (AB)²/(PQ)² = (BC)²/(QR)² = (AC)²/(PR)²

Calculation:

Let the length of BC be x.

ΔABC ~ ΔPQR

ar(ΔABC)/ar(ΔPQR) = (BC)2/(QR)²

⇒ (25/49) = (x²)/(3)²

⇒ (25/49) × 9 = x²

⇒ (5/7) × 3 = x

⇒ x = 15/7

∴ The length of the side BC is 15/7.