# ML Aggarwal Solutions Class 10 Mathematics Solutions for Similarity Exercise 13.3 in Chapter 13 - Similarity

Question 2 Similarity Exercise 13.3

Given that ∆s ABC and PQR are similar.

Find: The ratio of the area of ∆ABC to the area of ∆PQR if their corresponding sides are in the ratio 1 : 3.

Solution:-

The square of any ratio between any two corresponding sides of two similar triangles is equal to the ratio of their areas.

From the question it is given that,

The area of ∆ABC to the area of ∆PQR if their corresponding sides are in the ratio 1 : 3

Then, ∆ABC ~ ∆PQR

area of ∆ABC/area of ∆PQR = BC2/QR2

So, BC : QR = 1 : 3

Therefore, ∆ABC/area of ∆PQR = 12/32

= 1/9

Hence the ratio of the area of ∆ABC to the area of ∆PQR is 1: 9

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