1.

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 cm2. 96 cm3. 100 cm4. 112 cm

Answer» 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. 



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