# If ∆ABC and ∆DEF are similar triangles such that AB = 3 cm,

Question:

If ∆ABC and ∆DEF are similar triangles such that AB = 3 cm, BC = 2 cm, CA = 2.5 cm and EF = 4 cm, write the perimeter of ∆DEF.

Solution:

GIVEN: ΔABC and ΔDEF are similar triangles such that AB = 3cm, BC = 2cm, CA = 2.5cm and EF = 4cm.

TO FIND: Perimeter of ΔDEF.

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

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

$\frac{3}{2}=\frac{D E}{4}$

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

Similarly,

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

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

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

Perimeter of $\triangle \mathrm{DEF}=\mathrm{DE}+\mathrm{EF}+\mathrm{DF}$

$=6+4+5$

$=15 \mathrm{~cm}$