Question

If ΔABC ~ ΔDEF, AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, then the perimeter of ΔABC is ______.

Answer 1

If ΔABC ~ ΔDEF, AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, then the perimeter of ΔABC is 18 cm.

Explanation:

Since ΔABC ~ ΔDEF, corresponding sides are proportional `((AB)/(DE) = (BC)/(EF) = (CA)/(FD))`.

`(AB)/(DE) = 4/6 = 2/3`

So `BC = 2/3 xx 9 = 6` cm and `CA = 2/3 xx 12 = 8` cm.

Perimeter = 4 + 6 + 8

= 18 cm