A rectangle has length five times its breadth and its perimeter is $70\text{ cm}$. Which area is larger, the rectangle or a square with side $8\text{ cm}$?

Step-by-step solution

1. Let the breadth of the rectangle be $x$ cm. Then the length is $5x$ cm.
2. Use the perimeter formula: $2(\text{length}+\text{breadth})=70$. Substituting gives $2(5x+x)=70⟹12x=70⟹x=\frac{70}{12}=\frac{35}{6}\text{ cm}$.
3. Compute the rectangle's area: $A_{\text{rect}}=\text{length}\times \text{breadth}=5x\times x=5x^2=5{\left(\frac{35}{6}\right)}^2=5\times \frac{1225}{36}=\frac{6125}{36}\approx 170.14{\text{ cm}}^2$.
4. Compute the square's area: $A_{\text{sq}}=8^2=64{\text{ cm}}^2$.
5. Compare the two areas: $170.14$ cm² vs $64$ cm². The rectangle's area is larger.
6. Conclusion: The rectangle has the larger area.

Concept tested: Comparing areas with algebraic expressions

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