Question

The areas of two similar triangle ABC and PQR are in the ratio 9:16.if BC=4.5cm, find the lenght of QR.

Answer 1

Area  of triangle ABC/Area  of triangle PQR=(BC)(BC)/(QR)(QR)

9/16=(4.5)(4.5)/QR*QR

9/16=20.25/QR*QR

QR*QR=16*20.25/9

QR*QR=36

=QR=6cm.

Answer 2

Answer:

6 cm

Step-by-step explanation:

The areas of two similar triangle ABC and PQR are in the ratio 9:16

Theorem : the ratio of the area of the two similar triangles is equal to the ratio of the square of the corresponding sides of the triangle

So, $\frac{9}{16}=\frac{BC^2}{QR^2}$

BC = 4.5

$\frac{9}{16}=\frac{BC^2}{QR^2}$

$\frac{9}{16}=\frac{4.5^2}{QR^2}$

$QR^2=\frac{4.5^2}{\frac{9}{16}}$

$QR^2=36$

$QR=\sqrt{36}$

$QR=6$

Hence the length of QR is 6 cm