Question

The perimeters of two similar triangles are 24 cm and 18 cm respectively. If one side of first triangle is 8 cm, what is the corresponding-side of the other triangle?

Answer 1

Let ABC,DEF be two triangles
$△ABC\sim △DEF$
$\therefore \frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=K$
$\therefore AB=K.DE,BC=K.EF,AC=K.DF$
$\therefore AB+BC+AC=K(DE+EF+DF)$
$\Rightarrow \frac{AB+BC+AC}{DE+EF+DF}=K$
Given,
$AB+BC+AC=24㎝$
$DE+EF+DF=18㎝$
$AB=8㎝$
$\therefore \frac{AB}{DE}=\frac{AB+BC+AC}{DE+EF+DF}=K$
$\Rightarrow \frac{8}{DE}=\frac{24}{18}$
$\Rightarrow DE=6㎝$
Answer:$6㎝$