ΔABC ~ ΔDEF such that ar(ΔABC) = 64 cm 2 and ar(ΔDEF) = 169 cm 2 . If BC = 4 cm, find EF.

Question

Philoid · Accepted Answer

We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

i.e. ar(ABC)/ar(DEF) = (BC/EF)²

Substituting the given values, we get

⇒ 64cm²/169cm² = (4cm/EF cm)²

⇒ 64/169 = 16/EF²

⇒ EF² = 42.25

⇒ EF = 6.5cm

6.5 cm