If triangle ABC sim triangle PQR, with frac{text{Area}(triangle ABC)}{text{Area}(triangle PQR)} = frac{9}{16} and BC = 4.5 cm, then the length of QR…

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. So, $\frac{\text{Area}(\triangle ABC)}{\text{Area}(\triangle PQR)} = \left(\frac{BC}{QR}\right)^2$. Thus, $\frac{9}{16} = \left(\frac{4.5}{QR}\right)^2$. Taking square roots, $\frac{3}{4} = \frac{4.5}{QR}$, which gives $QR = \frac{4.5 \times 4}{3} = 6$ cm.