SOLUTION: What is the length and width of a rectangle whose area is 16cm2 and whose perimeter is 18cm

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Question 431605: What is the length and width of a rectangle whose area is 16cm2 and whose perimeter is 18cm
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
If the area of the rectangle is 16cm2, then L X W=16. Also, 2L+2W=18.
2L+2W=18
2L=18-2W
L=9-W
Substituting for L, we get:
(9-W)W=16
9W-W2=16
0=W2-9W+16
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-9x%2B16+=+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=%28-9%29%5E2-4%2A1%2A16=17.

Discriminant d=17 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--9%2B-sqrt%28+17+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+17+%29%29%2F2%5C1+=+6.56155281280883
x%5B2%5D+=+%28-%28-9%29-sqrt%28+17+%29%29%2F2%5C1+=+2.43844718719117

Quadratic expression 1x%5E2%2B-9x%2B16 can be factored:
1x%5E2%2B-9x%2B16+=+1%28x-6.56155281280883%29%2A%28x-2.43844718719117%29
Again, the answer is: 6.56155281280883, 2.43844718719117. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-9%2Ax%2B16+%29