Question

It is given that ∆ABC ~ ∆EDF such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm. Find the lengths of the remaining sides of the triangles.

Answer 1

Given,

∆ABC ∼ ∆EDF,

So the corresponding sides of ∆ABC and ∆EDF are in the same ratio.

i.e., `("AB")/("ED") = ("AC")/("EF") = ("BC")/("DF")`   ...(i)

Also,

AB = 5 cm,

AC = 7 cm,

DF = 15 cm

And DE = 12 cm

On putting these values in equation (i), we get

`5/12 = 7/("EF") = ("BC")/15`

On taking first and second terms, we get

`5/12 = 7/("EF")`

⇒ EF = `(7 xx 12)/5` = 16.8 cm

On taking first and third terms, we get

`5/12 = ("BC")/15`

⇒ BC = `(5 xx 15)/12` = 6.25 cm

Hence, lengths of the remaining sides of the triangles are EF = 16.8 cm and BC = 6.25 cm.