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

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KollegeApply · Accepted Answer

If ∆ABC ~ ∆QRP, (ar(ABC))/(ar(PQR)) = $\frac{9}{4}$, 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. $\therefore$ `("ar(∆ABC)")/("ar(∆QRP)") = ("BC")^2/("RP")^2 But, ("ar(∆ABC)")/("ar(∆PQR)") = $\frac{9}{4}$ ...[Given] $\Rightarrow$ (15)^2/("RP")^2 = $\frac{9}{4}$` ...[∵ BC = 15 cm, given] $\Rightarrow$ (RP)2 = (225 xx 4)/9 = 100 $\therefore$ RP = 10 cm [Solution diagram: 270214_solution_1.png]

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