SOLUTION: the combined area of a square and a rectangle is 148 square centimeters. the width of the rectangle is 2 centimeters more than the length of a side of the square,and the length of

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Question 489405: the combined area of a square and a rectangle is 148 square centimeters. the width of the rectangle is 2 centimeters more than the length of a side of the square,and the length of the rectangle is 2 centimeters more than its width. find the dimensions of the square and the rectangle.
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
They're both squares.
n2+(n+2)2=148
n2+n2+4n+4=148
2n2+4n-144=0
n2+2n-72=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-72+=+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=%282%29%5E2-4%2A1%2A-72=292.

Discriminant d=292 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+292+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+292+%29%29%2F2%5C1+=+7.54400374531753
x%5B2%5D+=+%28-%282%29-sqrt%28+292+%29%29%2F2%5C1+=+-9.54400374531753

Quadratic expression 1x%5E2%2B2x%2B-72 can be factored:
1x%5E2%2B2x%2B-72+=+1%28x-7.54400374531753%29%2A%28x--9.54400374531753%29
Again, the answer is: 7.54400374531753, -9.54400374531753. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-72+%29

Throwing out the negative answer, we get the width and length of the smaller square to be 7.544003745 cm, and the width and length of the larger square to be 9.54400374531753 cm..