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# Given Triangle Abc ~ Triangle Pqr, If (Ab)/(Pq) = 1/3, Then Find (Ar Triangle Abc)/(Ar Triangle Pqr) - CBSE Class 10 - Mathematics

#### Question

Given triangle ABC ~ triangle PQR, if (AB)/(PQ) = 1/3, then find (ar  triangle ABC)/(ar triangle PQR)

#### Solution 1

(A(triangle ABC))/(A(triangle PQR)) = (AB)^2/(PQ)^2

(Ratio of area of the similar triangle is equal to the square of their proportional sides)

(A(triangle ABC))/(A(triangle PQR)) = (1/3)^2 = 1/9

#### Solution 2

Given triangle ABC ~ triangle PQR

Also (AB)/(PQ) = 1/3

We know if two triangles are similar then the ratio of the areas of two similar triangles is equal to the square of the ratio of their  corresponding sides

(ar triangle ABC)/(ar triangle PQR) = ((AB)/(PQ))^2 = (1/3)^2 = 1/9

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Solution Given Triangle Abc ~ Triangle Pqr, If (Ab)/(Pq) = 1/3, Then Find (Ar Triangle Abc)/(Ar Triangle Pqr) Concept: Similarity of Triangles.
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