# The areas of two similar triangles ABC and DEF are 144cm2 and 81cm2, respectively. If the longest side of larger triangle ABC is 36 cm, then the longest side of the smaller triangle DEF is (1) 20 cm (2) 26 cm (3) 27 cm (4) 30 cm

Answer: (3) 27 cm

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

Ratio of areas = 144:81

Ratio of sides = 12:1

Let the longest side be X

Then

36 : X = 12:9

X = (36 × 9)/12

X = 27 cm

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