Q4 of 168 Page 5

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.

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


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