Question

∆ABC ~ ∆DEF for the correspondence XYZ,EDF. if XY=3, YZ=4, ZX=6 and DF=12, find the perimeter of ∆DEF.

Answer 1

Answer:

The perimeter of ∆DEF=26 units

Step-by-step explanation:

Concept used:

The ratio of perimeter of two similar triangles is equal to ratio otheir corresponding sides.

Given:

∆XYZ and ∆DEF are similar

Then,

$\frac{Perimeter\:of\:∆XYZ}{Perimeter\:of\:∆DEF}=\frac{XZ}{DF}$

$\implies\:\frac{XY+YZ+ZX}{Perimeter\:of\:∆DEF}=\frac{XZ}{DF}$

$\implies\:\frac{3+4+6}{Perimeter\:of\:∆DEF}=\frac{6}{12}$

$\implies\:\frac{13}{Perimeter\:of\:∆DEF}=\frac{1}{2}$

$\implies\:Perimeter\:of\:∆DEF=26\:units$