A rectangular garden is to have an area of $150{\text{m}}^2$. Its length is $5\text{m}$ more than its breadth. Find the length and breadth of the garden.

Step-by-step solution

1. Let the breadth be $x$ metres; then length = $x+5$ metres.
2. Area = length $\times$ breadth, so $x(x+5)=150$.
3. Expand: $x^2+5x-150=0$.
4. Factorise the quadratic: find two numbers whose product is $-150$ and sum $5$; they are $15$ and $-10$.
5. Rewrite as $x^2+15x-10x-150=0$ and factor: $x(x+15)-10(x+15)=0$.
6. Factor out $(x+15)$: $(x-10)(x+15)=0$.
7. Set each factor to zero: $x-10=0$ or $x+15=0$. Reject negative breadth, so $x=10$.
8. Hence breadth $=10$ m and length $=10+5=15$ m.

Concept tested: Word problem leading to quadratic

Published 24 August 2026 · How this solution was prepared and checked

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