Question

$\Delta$ABC and $\Delta$PQR are similar triangles. If AB = 4 cm, BC = 5 cm, AC = 2 cm, and PQ = 8 cm, find the perimeter of the $\Delta$PQR.

• A. 16 cm
• B. 22 cm
• C. 28 cm
• D. 30 cm

Answer 1

The correct option is B 22 cm

Given:
$\Delta$ABC and $\Delta$PQR are similar triangles. AB = 4 cm, BC = 5 cm, AC = 2 cm, and PQ = 8 cm

We know that corresponding sides of similar triangles are proportional.

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

$\frac{8}{4}=\frac{QR}{5}=\frac{PR}{2}$
So, QR = 10 cm and PR = 4 cm

Perimeter of $\Delta$PQR = PQ + QR + PR
Perimeter of $\Delta$PQR = 8 + 10 + 4 = 22 cm