The perimeter of ΔXYZ is 126 units.
Solution:
Given ΔPQR [tex]\sim[/tex] 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.
[tex]$\Rightarrow\frac{PQ}{XY} = \frac{\text{Perimeter of} \Delta PQR}{\text{Perimeter of} \Delta XYZ}[/tex]
[tex]$\Rightarrow\frac{5}{30} = \frac{21}{\text{Perimeter of} \Delta XYZ}[/tex]
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.
