Question 24334: Hi there, i'm having trouble with this word problem and i was wondering if one of you could help me... i already tried to do some of it but im not quite sure i'm doing it right.
Question:
A rectangular flower garden is planted in a rectangular yard that is 16 m by 12 m. The garden occupies 1\6 of the area of the yard and leaves a uniform strip of grass around the edges. Find the dimensions of the garden.
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This is what I have already tried but I don't think I am doing it right. If you could show me how to do this problem or correct me that would be great.
16-x+12-x+x2 <--(x squared.) = 160
Answer by kev82(151)   (Show Source):
You can put this solution on YOUR website! Hi,
I don't think it's a very good question because it's not clear what is meant by uniform strip. I'm going to assume that it means the strip is the same width all the way round the garden.
You are definately doing something right, because you have a quadratic, and the equation is going to be a quadratic. I can't say any more because I don't know what your 'x' is.
Let's call the width of the uniform strip  . Now the garden has this strip on all sides, so the width of the garden is going to be  and the height is going to be  . I'm useless at computer drawing, but this picture has taken me ten minutes to do, so hopefully gives you the idea.
Back to the problem, we know that the area of the garden (12-2x)) is a sixth the area of the yard  . So we get the equation
(12-2x)=32)
I'm sure you can solve it from now. Remember, you'll get two solutions for x. If you check you'll see that one of them doesn't make sense, so the other one must be right.
Also don't forget the problem asked for the dimensions of the garden, not x. So you're still not quite finished.
Hope this helps.
Kev
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