The areas of two similar triangles ABC and MR are in the ratio 9 : 16. If BC 4.5 cm find the length of QR.

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Solution

if triangles ABC and PQR are similar triangles.

$\frac{a r e a (△ A B C)}{a r e a (△ P Q R} = \frac{B C^{2}}{Q R^{2}}$

$\frac{9}{16} = \frac{{4.5}^{2}}{Q R^{2}}$

$(\frac{3}{4})^{2} = \frac{{4.5}^{2}}{Q R^{2}}$

$\frac{4.5}{Q R} = \frac{3}{4}$

$3 \times Q R = 4.5 \times 4$

3QR=18

QR= $\frac{18}{3} = 6 c m$

thus the length of QR is 6 cm.

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The areas of two similar triangles ABC and MR are in the ratio 9 : 16. If BC 4.5 cm find the length of QR.

if triangles ABC and PQR are similar triangles. area(△ABC)area(△PQR=BC2QR2 916=4.52QR2 (34)2=4.52QR2 4.5QR=34 3×QR=4.5×4 3QR=18 QR= 183=6cm thus the length of QR is 6 cm.