Let ∆ABC ~ ∆XYZ and their areas be, respectively, 64 cm² and 81 cm². If YZ = 18 cm, find BC.

Given: ΔABC ~ ΔXYZ

Area of ΔABC = 64 cm²

Area of ΔXYZ = 81 cm²

YZ = 18 cm

As we know, if two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides.

$\therefore \frac{\mathrm{Area} \mathrm{of} △\mathrm{ABC}}{\mathrm{Area} \mathrm{of} △\mathrm{XYZ}}=\frac{{\mathrm{BC}}^2}{{\mathrm{YZ}}^2}$

$\Rightarrow \frac{64}{81}=\frac{{\mathrm{BC}}^2}{{18}^2}$

$\Rightarrow \frac{\mathrm{BC}}{18}=\sqrt{\frac{64}{81}}$

$\Rightarrow \frac{\mathrm{BC}}{18}=\frac{8}{9}$

$\Rightarrow \mathrm{BC}=\frac{8}{9}\times 18$

$\Rightarrow \mathrm{BC}=16 \mathrm{cm}$