Context: Right angle at $C$. $AB = \sqrt{89}$, $AC = 8$, $CE = 24$. Find area of $\triangle ADE$.

Answer: $320$

Why: $BC = \sqrt{89 - 64} = 5$. $AE = 8 + 24 = 32$. $\triangle ABC \sim \triangle ADE$ (AA), scale $= 32/8 = 4$. $DE = 5 \times 4 = 20$. Area $= \frac{1}{2}(32)(20) = 320$.

Traps: Using $BC = 5$ as $DE$ directly (forgetting scale factor). Computing area of small triangle instead of large.