# If ∆ABC and ∆DEF are similar such that 2AB = DE and BC = 8 cm, then EF =

Question:

If ∆ABC and ∆DEF are similar such that 2AB = DE and BC = 8 cm, then EF =

(a) 16 cm
(b) 12 cm
(c) 8 cm
(d) 4 cm

Solution:

Given: ΔABC and ΔDEF are similar triangles such that 2AB = DE and BC = 8 cm.

To find: EF

We know that if two triangles are similar then there sides are proportional.

Hence, for similar triangles ΔABC and ΔDEF

$\frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{EF}}=\frac{\mathrm{CA}}{\mathrm{FD}}$

$\frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{EF}}$

$\frac{1}{2}=\frac{8}{E F}$

$E F=16 \mathrm{~cm}$

Hence the correct answer is $(a)$.