SOLUTION: The length of the table top is 5m greater than the width. The area is 66m2. Find the Dimensions of the table top

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Question 448678: The length of the table top is 5m greater than the width. The area is 66m2. Find the Dimensions of the table top
Answer by chriswen(106) About Me  (Show Source):
You can put this solution on YOUR website!
Let x m be the width of the table top.
Let x+5 m be the length of the table top.
...
A=l*w
66=(x)(x+5)
66=x^2+5x
0=x^2+5x-66
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B5x%2B-66+=+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=%285%29%5E2-4%2A1%2A-66=289.

Discriminant d=289 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+289+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+289+%29%29%2F2%5C1+=+6
x%5B2%5D+=+%28-%285%29-sqrt%28+289+%29%29%2F2%5C1+=+-11

Quadratic expression 1x%5E2%2B5x%2B-66 can be factored:
1x%5E2%2B5x%2B-66+=+1%28x-6%29%2A%28x--11%29
Again, the answer is: 6, -11. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-66+%29

The answer must be positive so,
x=6
x+5=11
...
Therefore, the dimensions of the table top is 6m by 11m.