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.

--------------------
x-9 | |
| |
| |
--------------------
x

Found 2 solutions by nerdybill, jim_thompson5910:
Answer by nerdybill(7384)   (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)   (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.


Start with the area of a rectangle formula


Plug in , and


Distribute


Subtract 220 from both sides.


Notice we have a quadratic equation in the form of where , , and


Let's use the quadratic formula to solve for x


Start with the quadratic formula


Plug in , , and


Negate to get .


Square to get .


Multiply to get


Rewrite as


Add to to get


Multiply and to get .


Take the square root of to get .


or Break up the expression.


or Combine like terms.


or Simplify.


So the possible answers are or

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


So the length is and the width is


==============================================

Answer:

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

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