Question

Let ∆ ABC ∽ ∆ DEF and their areas be respectively, 64 cm² and 121 cm². If EF = 15⋅4 cm, find BC.

Answer 1

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.