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Let ∆ ABC ∽ ∆ DEF and their areas be respectively, 64 cm^{2} and 121 cm^{2}. If EF = 15⋅4 cm, find BC.

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#### Solution

Given: △ABC ~ △DEF

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

`("arΔABC")/("arΔDEF") = ("BC"/"EF")^2`

⇒ `64/121 = ("BC"/15.4)^2`

⇒ `(8/11)^2 = ("BC"/15.4)^2`

⇒ `8/11 = "BC"/15.4`

⇒ BC = `(8 xx 15.4)/11` = 11.2 cm

Thus, BC = 11.2 cm.

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