# It is given that ΔABC ~ ΔPQR, with BCQR=13. Then, ar(PRQ)ar(BCA) is equal to ______. - Mathematics

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It is given that ΔABC ~ ΔPQR, with (BC)/(QR) = 1/3. Then, (ar(PRQ))/(ar(BCA)) is equal to ______.

• 9

• 3

• 1/3

• 1/9

#### Solution

It is given that ΔABC ~ ΔPQR, with (BC)/(QR) = 1/3. Then, (ar(PRQ))/(ar(BCA)) is equal to 9.

Explanation:

Given, ∆ABC ~ ∆QR and (BC)/(QR) = 1/3

We know that, the ratio of the areas of two similar triangles is equal to square of the ratio of their corresponding sides.

∴ (ar(∆PRQ))/(ar(∆BCA)) = (QR)^2/(BC)^2 = ((QR)/(BC))^2

= (3/1)^2

= 9/1

= 9

Concept: Similarity of Triangles
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 6 Triangles
Exercise 6.1 | Q 8 | Page 62
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