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 triangle.

Given,

∆ABC ∼ ∆EDF,

So the corresponding sides of ∆ABC and ∆EDF are in the same ratio. (Property of similar triangle)

AB/ED = AC/EF = BC/DF ….(i)

Also,

AB = 5cm, AC = 7cm (given)

DF = 15cm and DE = 12cm (given)

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

On taking first and second terms, we get,

On taking first and third terms, we get,

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