The areas of two similar triangles are 169 cm 2 and 121 cm 2 respectively. If the longest side of the larger triangle is 26 cm, find the longest side of the smaller triangle.

Question

Philoid · Accepted Answer

We have,

ΔABC ~ Δ PQR

Area (ΔABC) = 169cm²

Area (PQR) = 121 cm²

And AB = 26 cm

By area of similar triangle theorem

Area of ΔABC/Area of ΔPQR = AB² /PQ²

Or, 169/125 = 26²/ PQ²

Or, 13/11 = 26/PQ (Taking square root)

Or, PQ = 11/13 x 26

Or, PQ = 22cm

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.

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.