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A charity trust decides to build a rectangular hall having an area of $300\text{ m}^2$. The length of the hall is one metre more than twice its width. Find the length and breadth of the hall.
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Let width be $x\text{ m}$ and length be $(2x + 1)\text{ m}$ [$\frac{1}{2}$ mark]
A.T.Q. $(2x + 1)x = 300$ [$1\frac{1}{2}$ marks]
$2x^2 + x - 300 = 0$ [$1\frac{1}{2}$ marks]
$(x - 12)(2x + 25) = 0$
$x = 12$ [$1$ mark]
(Rejecting $x = -\frac{25}{2}$)
$\text{length} = 25\text{ m and width} = 12\text{ m}$ [$\frac{1}{2}$ mark]
A.T.Q. $(2x + 1)x = 300$ [$1\frac{1}{2}$ marks]
$2x^2 + x - 300 = 0$ [$1\frac{1}{2}$ marks]
$(x - 12)(2x + 25) = 0$
$x = 12$ [$1$ mark]
(Rejecting $x = -\frac{25}{2}$)
$\text{length} = 25\text{ m and width} = 12\text{ m}$ [$\frac{1}{2}$ mark]