SOLUTION: area of a rectangle= 220 square feet. find the diminensions of the figure. ----------- -------- x-9 | | |

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Question 178500: area of a rectangle= 220 square feet. find the diminensions of the figure.

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x-9 | |
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x
Found 2 solutions by nerdybill, jim_thompson5910:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Since we know that area of any rectangle is:
"width" * "length"
.
We then have:
x(x-9) = 220
x^2 - 9x = 220
x^2 - 9x - 220 =0
(x-20)(x+11) = 0
.
x = {20, -11}
.
We can toss out the negative solution leaving us with:
x = 20 feet
x-9 = 11 feet
.
Therefore, the dimensions are:
20 feet by 11 feet

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let Length=x and Width=x-9 Note: the order does not matter, but the length is usually the longer of the two.


A=LW Start with the area of a rectangle formula


220=x%28x-9%29 Plug in A=220, L=x and W=x-9


220=x%5E2-9x Distribute


0=x%5E2-9x-220 Subtract 220 from both sides.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-9, and c=-220


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-9%29+%2B-+sqrt%28+%28-9%29%5E2-4%281%29%28-220%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-9, and c=-220


x+=+%289+%2B-+sqrt%28+%28-9%29%5E2-4%281%29%28-220%29+%29%29%2F%282%281%29%29 Negate -9 to get 9.


x+=+%289+%2B-+sqrt%28+81-4%281%29%28-220%29+%29%29%2F%282%281%29%29 Square -9 to get 81.


x+=+%289+%2B-+sqrt%28+81--880+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-220%29 to get -880


x+=+%289+%2B-+sqrt%28+81%2B880+%29%29%2F%282%281%29%29 Rewrite sqrt%2881--880%29 as sqrt%2881%2B880%29


x+=+%289+%2B-+sqrt%28+961+%29%29%2F%282%281%29%29 Add 81 to 880 to get 961


x+=+%289+%2B-+sqrt%28+961+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%289+%2B-+31%29%2F%282%29 Take the square root of 961 to get 31.


x+=+%289+%2B+31%29%2F%282%29 or x+=+%289+-+31%29%2F%282%29 Break up the expression.


x+=+%2840%29%2F%282%29 or x+=++%28-22%29%2F%282%29 Combine like terms.


x+=+20 or x+=+-11 Simplify.


So the possible answers are x+=+20 or x+=+-11

However, since you can't have a negative length, this means that only solution is x=20


So the length is L=x=20 and the width is W=x-9=20-9=11


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Answer:

So the length is 20 ft and the width is 11 ft