Question

TRIANGLE ABC IS SIMILAR TO TRIANGLE PQR AND AREA OF TRIANGLE ABC = 4 AREA OF TRIANGLE PQR.IF BC =12CM, FIND QR?

Answer 1

We know for similar triangles

AREA OF TRIANGLE ABC/AREA OF TRIANGLE PQR = BC^2/QR^2

4= 12^2/QR^2

QR^2 = 144/4 = 36

>> QR = 6

Answer 2

Answer:

The measure of QR is 6 cm.

Step-by-step explanation:

It is given that

$\triangle ABC\sim \triangle PQR$

The corresponding sides of similar triangles are proportional and the corresponding angles are same.

The ratio of  areas of two similar triangles is the square of the ratio of their sides.

$\frac{\text{Area of }\triangle ABC}{\text{Area of }\triangle PQR}=(\frac{BC}{QR})^2$

It is given that

$\text{Area of }\triangle ABC=4\times \text{Area of }\triangle PQR$

$\frac{\text{Area of }\triangle ABC}{\text{Area of }\triangle PQR}=4$

$4=(\frac{12}{QR})^2$

Take square root both sides

$2=\frac{12}{QR}$

$QR=\frac{12}{2}=6$

Therefore the measure of QR is 6 cm.