Question

A ABC - A PQR. AB = 6 cm, BC = 4 cm,
AC = 8 cm and PQ = 9 cm. What is
the perimeter of A PQR?
a) 54 cm
b) 27cm
c) 18 cm
d) 36 cm​

Answer 1

Answer:

Given:

ΔABC∼ΔPQR.

Since they are similar, the ratio of the sides of the two triangles are equal.

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

• AB = 6 cm
• BC = 4 cm
• AC = 8 cm
• PQ = 9 cm

First, use this formula:

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

$\frac{6}{9} =\frac{4}{QR}$

$QR=\frac{9\times4}{6}$

$QR=6cm.$

Now, we know that PQ=9cm, QR=6cm, We need to find PR.

Use this formula to find PR:

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

$\frac{4}{6}= \frac{8}{PR}$

$PR=12cm.$

Now, we have PQ=9cm, QR=6cm, PR=12cm.

Thus, perimeter = PQ+QR+PR

= 9+6+12

= 27cm.

THUS, OPTION a IS CORRECT.

HOPE THIS HELPS :D