If △ABC ~ △QRP, ar(ABC)/ar(PQR) = 9/4, AB = 18 cm and BC = 15 cm, then PR is equal to
a. 10 cm
b. 12 cm
c. 20/3 cm
d. 8 cm

Solution:

Given, the triangles ABC and PQR are similar.

Area of ABC/Area of PQR = 9/4

The length of the sides

AB = 18 cm

BC = 15 cm

We have to find the length of PR.

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

So, area of ABC/area of PQR = BC²/RP²

9/4 = (15)²/RP²

Taking square root,

3/2 = 15/RP

On cross multiplication,

3(RP) = 15(2)

RP = 30/3

RP = 10 cm

Therefore, the length of PR is 10 cm.

✦ Try This: If △ABC ~ △QRP, ar(ABC)/ar(PQR) = 16/4, AB = 8 cm and BC = 11 cm, then PR is equal to

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6

NCERT Exemplar Class 10 Maths Exercise 6.1 Problem 11

If △ABC ~ △QRP, ar(ABC)/ar(PQR) = 9/4, AB = 18 cm and BC = 15 cm, then PR is equal to, a.10 cm, b. 12 cm, c. 20/3 cm, d. 8 cm

Summary:

If △ABC ~ △QRP, ar(ABC)/ar(PQR) = 9/4, AB = 18 cm and BC = 15 cm, then PR is equal to 10 cm

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