Question

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

Answer 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`

Answer 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`