Question

What is the perimeter of XY Z? please explain step by step

Answer 1

The perimeter of ΔXYZ is 126 units.

Solution:

Given ΔPQR $\sim$ ΔXYZ.

In ΔPQR,

PQ = 5, QR = 10, PR = 6

In ΔXYZ,  XY = 30

Perimeter of ΔPQR = PQ + QR + PR

                                = 5 + 10 + 6

                                = 21

Perimeter of ΔPQR = 21

To find the perimeter of ΔZYZ:

If two triangles are similar then the ratio of the perimeters of two similar triangles is same as the ratio of their corresponding sides.

$\Rightarrow\frac{PQ}{XY} = \frac{\text{Perimeter of} \Delta PQR}{\text{Perimeter of} \Delta XYZ}$

$\Rightarrow\frac{5}{30} = \frac{21}{\text{Perimeter of} \Delta XYZ}$

Do cross multiplication, we get

⇒ 5 × Perimeter of ΔXYZ = 30 × 21

⇒ 5 × Perimeter of ΔXYZ = 630

Divide by 5 on both sides of the equation.

⇒ Perimeter of ΔXYZ = 126

Hence the perimeter of ΔXYZ is 126 units.