A garden is in the shape of a rectangle, $20$m by $8$m. Around the outside is a border of uniform width and in the middle is a square pond. The area which is not occupied by either border or pond is 1$24 m^2$. Letting the width of border be $x$cm, find the equation. Solve the equation to find the value of $x$.
2026-04-01 05:41:48.1775022108
quadratic equation
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1
The solution provided in the last comment works if we assume that the side of the square pond is equal to $x$ as well. In this case, the rectangle without the borders has sides $20-2x$ and $8-2x$, and the area of the pond is $x^2$. Thus
$$(20-2x)(8-2x)-x^2=124$$
$$160-56x+4x^2-x^2=124$$
and then
$$3x^2-56x+36=0$$
whose solutions are $x=\frac{2}{3}$ (realistic for the context of the problem) and $18$.