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प्रश्न
If ∆ABC ~ ∆QRP, `(ar(ABC))/(ar(PQR)) = 9/4`, AB = 18 cm and BC = 15 cm, then PR is equal to ______.
पर्याय
10 cm
12 cm
`20/3` cm
8 cm
उत्तर
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
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