# If areas of similar ΔABC and ΔPQR are 196 cm2 and 289 cm2 respectively. If AB is 28 cm longer. What is the length of PQ?

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If areas of similar ΔABC and  ΔPQR are 196 cm2 and 289 cm2 respectively. If AB is 28 cm longer. What is the length of PQ?
1. 30 cm
2. 34 cm
3. 17 cm
4. 51 cm

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Correct Answer - Option 2 : 34 cm

Given:

ΔABC ∼ ΔPQR

Area of ΔABC = 196 cm2

Area of ΔPQR = 289 cm2

AB = 28 cm

Concept:

The ratio of the area of two similar triangles is proportional to the squares of the corresponding sides of both triangles.

Calculation:

The ratio of the area of two similar triangles is proportional to the squares of the corresponding sides of both triangles.

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

⇒ (196 cm2/289 cm2) = (28 cm/PQ)2

⇒ 14 cm/17 cm = 28 cm/ PQ

By cross multiplication

⇒ PQ = 34 cm

∴ The length of PQ is 34 cm.

The correct option is 2 i.e. 34 cm

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