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

From property of similar triangle,

We know that, corresponding sides of ∆ABC and ∆EDF are in the same ratio.

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

AB = 5cm, AC = 7cm

DF = 15cm and DE = 12cm

Substituting these values in equation (i), we get,

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

On taking `5/12 = 7/(EF)`, we get,

`5/12 = 7/(EF)`

EF = `(12 xx 7)/5` = 16.8 cm

On taking `5/12 = (BC)/15`, 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