# If ∆ABC ∼ ∆DEF such that DE = 3 cm, EF = 2 cm,

Question:

If ∆ABC ∼ ∆DEF such that DE = 3 cm, EF = 2 cm, DF = 2.5 cm, BC = 4 cm, then perimeter of ∆ABC is

(a) 18 cm
(b) 20 cm
(c) 12 cm
(d) 15 cm

Solution:

Given: ΔABC and ΔDEF are similar triangles such that DE = 3cm, EF = 2cm, DF = 2.5cm and BC = 4cm.

To find: Perimeter of ΔABC.

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

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

Substituting the values we get

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

$\frac{\mathrm{AB}}{4}=\frac{3}{2}$

$\mathrm{AB}=6 \mathrm{~cm}$.....$(1)$

Similarly,

$\frac{\mathrm{CA}}{\mathrm{BC}}=\frac{\mathrm{DF}}{\mathrm{EF}}$

$\frac{\mathrm{CA}}{4}=\frac{2.5}{2}$

$\mathrm{CA}=5 \mathrm{~cm}$.....(2)

Perimeter of $\triangle \mathrm{ABC}=\mathrm{AB}+\mathrm{BC}+\mathrm{CA}$

$=6+4+5$

$=15 \mathrm{~cm}$

Hence the correct option is $(d)$