Question

A triangle ABC with AB = 3 cm, BC = 6 cm and AC = 4 cm is enlarged to ΔDEF such that the longest side of ΔDEF = 9 cm. Find the scale factor and hence, the lengths of the other sides of ΔDEF.

Answer 1

Triangle ABC is enlarged to DEF.

So, the two triangles will be similar.

∴ `(AB)/(DE) = (BC)/(EF) = (AC)/(DF)`

Longest side in ΔABC = BC = 6 cm

Corresponding longest side in ΔDEF = EF = 9 cm

Scale factor = `(EF)/(BC) = 9/6 = 3/2 = 1.5`

∴ `(AB)/(DE) = (BC)/(EF) = (AC)/(DF) = 2/3`

`DE = 3/2 AB = 9/2 = 4.5  cm`

`DF = 3/2 AC = 12/2 = 6  cm`