Two similar triangles have their corresponding sides in the ratio 3:5. If the area of the smaller triangle is 27 cm², what is the area of the larger triangle?

Step-by-step solution

1. The ratio of areas equals the square of the ratio of corresponding sides: $(\frac{3}{5}{)}^2=\frac{9}{25}$
2. Let the area of the larger triangle be $A$. Set up proportion: $\frac{27}{A}=\frac{9}{25}$
3. Cross‑multiply: $27\times 25=9A$
4. Solve: $675=9A\Rightarrow A=75$

Concept tested: similar figures area ratio

Published 7 October 2026 · How this solution was prepared and checked