SOLUTION: The width of a rectangle is 4 cm less than its length. If the area of the rectangle is 87cm^2 what are the dimensions of the rectangle? Round to the nearest thousandth. I have

Algebra ->  Pythagorean-theorem -> SOLUTION: The width of a rectangle is 4 cm less than its length. If the area of the rectangle is 87cm^2 what are the dimensions of the rectangle? Round to the nearest thousandth. I have       Log On


   

Question 338556: The width of a rectangle is 4 cm less than its length. If the area of the rectangle is 87cm^2 what are the dimensions of the rectangle? Round to the nearest thousandth.
I have figured out the answer as
Length = 11.539
Width = 7.539
Just don't know the formula or how to solve, help would be greatly appreciated thank you.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The width of a rectangle is 4 cm less than its length. If the area of the rectangle is 87cm^2 what are the dimensions of the rectangle? Round to the nearest thousandth.
I have figured out the answer as
Length = 11.539
Width = 7.539
--------------------
Area = L*W
L = W+4
Area = (W+4)*W = 87
W^2 + 4W = 87
W^2 + 4W - 87 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B-87+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A1%2A-87=364.

Discriminant d=364 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+364+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+364+%29%29%2F2%5C1+=+7.53939201416946
x%5B2%5D+=+%28-%284%29-sqrt%28+364+%29%29%2F2%5C1+=+-11.5393920141695

Quadratic expression 1x%5E2%2B4x%2B-87 can be factored:
1x%5E2%2B4x%2B-87+=+%28x-7.53939201416946%29%2A%28x--11.5393920141695%29
Again, the answer is: 7.53939201416946, -11.5393920141695. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-87+%29

----------------
W = x (ignore the negative solution)
W = 7.53939 ...
L = 11.53939...