Question

Holaa...
Here is my question...

If ∆ ABC ~∆ PQR then prove that perimeter of ∆ABC/perimeter of ∆PQR = AB/PQ

Answer 1

Answer with Step-by-step explanation:

We are given that

$\triangle ABC\sim\triangle PQR$

We have to prove that

Perimeter of triangle ABC/perimeter of triangle PQR=$\frac{AB}{PQ}$

We know that when two triangles similar then

$\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}$

Adding three equations then we get

$\frac{AB+BC+AC}{PQ+QR+PR}=\frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}$

$\frac{Perimeter\;of\;triangle ABC}{perimeter\;of\;triangle\;PQR}=\frac{AB}{PQ}$

Because perimeter of triangle=Sum of sides of triangle

Hence, proved.