A right triangle has legs 6 cm and 8 cm. A rectangle has length 12 cm and the same area as this triangle. Find the perimeter of the rectangle.

Step-by-step solution

1. Area of a right triangle is $\frac{1}{2}\times {\text{leg}}_1\times {\text{leg}}_2$ because the base and height are the legs.
2. Compute the triangle area: $\frac{1}{2}\times 6\times 8=24$ cm${}^2$.
3. The rectangle area equals the triangle area, so $A_{\text{rect}}=24$ cm${}^2$ and $A_{\text{rect}}=\text{length}\times \text{width}$.
4. Given length $=12$ cm, solve for width: $12\times \text{width}=24⟹\text{width}=\frac{24}{12}=2$ cm.
5. Perimeter of a rectangle is $2(\text{length}+\text{width})$ because we sum all four sides.
6. Compute: $2(12+2)=2\times 14=28$ cm.
7. Hence the rectangle’s perimeter is $28$ cm.

Concept tested: Perimeter from area

Published 13 October 2026 · How this solution was prepared and checked