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Question
Let ∆ ABC ∽ ∆ DEF and their areas be respectively, 64 cm2 and 121 cm2. If EF = 15⋅4 cm, find BC.
Solution
Given:
Δ ABC ∼ Δ DEF
We know the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
`("ar"Δ"ABC")/("ar"Δ"DEF") = ("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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