If the areas of two similar triangles ABC and PQR are in the ratio 9 : 16 and BC = 4.5 cm, what is the length of QR?

Given ΔABC ~ ΔPQR, ar (ΔABC): ar (ΔPQR) = 9: 16 and BC = 4.5 cm

We know that the ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

⇒ QR² = 2.25 (16)

⇒ QR² = 36

⇒ QR = 6

∴ The length of QR is 6 cm.