Question

ΔABC and ΔPQR are similar to each other. If the ratio of area of ΔABC and ΔPQR is 1 ∶ 16, and the length of side AC is 28 cm, then find the length of PR.
1. 156 cm
2. 96 cm
3. 100 cm
4. 112 cm

Answer 1

Correct Answer - Option 4 : 112 cm

Given:

ΔABC and ΔPQR are similar to each other.

Ratio of area of ΔABC and ΔPQR = 1 : 16

Length of side AC = 28 cm

Concept:

Relation among areas, side of similar triangles ABC and PQR

(Area of ΔABC and ΔPQR) = (AB/PQ)² = (BC/QR)² = (AC/PR)²

Calculation:         

Let PR be x cm

(Area of ΔABC and ΔPQR) = (AC/PR)²

⇒ (1/16) = (28/x)²

Taking square root on both the sides

⇒ √(1/16) = √(28/x)²

⇒ (1/4) = (28/x)

⇒ x = 28 × 4

⇒ x = 112 cm

∴ The length of PR is 112 cm.