Two similar triangles have corresponding side lengths in the ratio 4:7. If the area of the smaller triangle is 96 cm², find the area of the larger triangle.

Step-by-step solution

1. Scale factor between the triangles = 7 ÷ 4 = 1.75.
2. Area scales as the square of the side ratio, so area ratio = $(7/4{)}^2=49/16$.
3. Multiply smaller area by this ratio: $96\times 49/16$.
4. Simplify: $96÷16=6$, then $6\times 49=294$.
5. Thus the area of the larger triangle is 294 cm².

Concept tested: area ratio of similar figures

Published 10 October 2026 · How this solution was prepared and checked