A rectangular community garden has width $x$ metres and length $(x+5)$ metres. Its area is \(50\

Question

A rectangular community garden has width $x$ metres and length $(x+5)$ metres. Its area is $50\,\text{m}^2$. Form an equation in $x$ and show that it simplifies to $x^2+5x-50=0$. Solve the equation. Hence, find the dimensions of the garden. Explain why one of the solutions is rejected.

Accepted Answer

(a) $x^2+5x-50=0$; (b) $x=5$ or $x=-10$; (c) $5\,\text{m}$ by $10\,\text{m}$.

Solution:

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