#### 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`

Is there an error in this question or solution?

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