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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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