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Question
The areas of two similar triangles are 169 cm2 and 121 cm2 respectively. If the longest side of the larger triangle is 26 cm, find the longest side of the smaller triangle.
Solution
We have,
ΔABC ~ ΔPQR
Area(ΔABC) = 169 cm2
Area(ΔPQR) = 121 cm2
And AB = 26 cm
By area of similar triangle theorem
`("Area"(triangleABC))/("Area"(trianglePQR))="AB"^2/"PQ"^2`
`rArr169/121=26^2/"PQ"^2`
`rArr13/11=26/"PQ"` [Taking square root]
`rArr"PQ"=11/13xx26=22` cm
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