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 $x$.
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Did you try sketching a diagram? – Jack Oct 26 '14 at 06:24
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@Jack I have tried but the diagram is weird – mathlover Oct 26 '14 at 06:28
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The question is unclear. Since the problem has an infinite number of solutions if the pond does not touch the border (can you see why?) I will assume it does. In terms of $x$, what would the area of the border be? The square? From that you should be able to form an equation. – Jack Oct 26 '14 at 06:50
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Do you have some other information about the side of the pond, in particular about its relation with $x$? – Anatoly Oct 26 '14 at 07:15
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@Anatoly no but the answer is 3x^2-56x+36=0 – mathlover Oct 26 '14 at 07:19
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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 $18$.
Anatoly
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