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A rectangular swimming pool with dimensions of 11m and 8m is built in a rectangular backyard. The area of the backyard is 1120m^2. If the strip of yard surrounding the pool is of uniform width, how wide is the strip?

So I tried to find a diagram but it doesn't seem to make sense because the backyard could have any dimensions...so i made the backyard 28 by 40 and then the answer would be 8.5 and 16 which isn't correct.

joko34
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    The strips should be the same width on all four sides. – Bobson Dugnutt Sep 29 '16 at 23:27
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    What do you mean by "which isn't correct"? Do you mean that that's not the answer that was given for the problem? Or do you mean that you see something wrong with that answer? If the latter, then clearly the backyard can't have any dimensions. – David Schwartz Sep 30 '16 at 00:10

2 Answers2

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Let the width of the strip of yard around the pool be $w$ metres. Then the whole yard is a rectangle that is $11 + 2w$ metres long and $8 + 2w$ metres wide - you can see this because there's a strip of width $w$ on the left of the pool, and a strip of equal size on the right, and similarly for the top and bottom.

So what's the area of the yard + pool? How can you relate that to stuff you know?

ConMan
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The information that the strip of yard surrounding the pool is of uniform width is important. The following calculatins are done in meters.

See the picture below ($w$ denotes the width and $m$ is meters; please note that some of the $w$'s are rotated!):

enter image description here

Let a and b be the dimensions of the rectangular backyard. You know that $a\cdot b = 1120$.

As the strip of surrounding yard is of uniform width, you also know that

$a - 11 = b - 8$,

because $(a - 11 = 2w = b - 8)$.

Now you can isolate a:

$a = b + 3$,

thus you must solve $(b+3)\cdot b = 1120$. The positive solution to this equation is $b=32$. Thus the width of the strip is $\frac{32-8}{2}$=12. Here I have just isolated $w$ in the equation $8 + 2w = b$, see the figure.

  • I think it would be more clear if you were to leave out the units (and perhaps just state in the beginning of the answer that you are working in units where a meter is defined to be $1$). As it is now, $m$ might look like some variable or unknown. – Bobson Dugnutt Sep 29 '16 at 23:31
  • You are right. I will leave it out and update with a figure in just a second. –  Sep 29 '16 at 23:33
  • The picture doesn't work – joko34 Sep 29 '16 at 23:43
  • It worked just a minute ago; I have tried to re-upload it just now. imgur.com is clearly not to be trusted. –  Sep 29 '16 at 23:44
  • Great. I hope it clarifies the situation. In general I recommend people to try and illustrate such problems. –  Sep 29 '16 at 23:45