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.

Answer 1

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