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MCQ

Fill in the Blanks

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

#### Options

10 cm

12 cm

`20/3` cm

8 cm

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#### Solution

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

**Explanation:**

Given, ∆ABC ~ ∆QRP, AB = 18 cm and BC = 15 cm

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

∴ `(ar(∆ABC))/(ar(∆QRP)) = (BC)^2/(RP)^2`

But, `(ar(∆ABC))/(ar(∆PQR)) = 9/4` .....[Given]

⇒ `(15)^2/(RP)^2 = 9/4` .....[∵ BC = 15 cm, given]

⇒ `(RP)^2 = (225 xx 4)/9` = 100

∴ RP = 10 cm

Concept: Similarity of Triangles

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