SOLUTION: Mouse Pad. The area of a rectangular mouse pad is 480 sq centimeters. Its length is 16 centimeters shorter than twice its width. What are the lengths and width of the mouse pad

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Question 77025: Mouse Pad. The area of a rectangular mouse pad is 480 sq centimeters. Its length is 16 centimeters shorter than twice its width.
What are the lengths and width of the mouse pad in centimeters.
I am having problems creating an equation for this to solve. we are doing factoring with standard form. I know the answer is 20 cm and 24 cm but what I have come up with is 2x(x-16)=480. I know that you have to get a 0 on the = side. Can you help me.
Kelly

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
if we let x=width, y=length we get
480=x%2Ay
where the length is
y=2x-16
480=x%2A%282x-16%29 Substitute 2x-16 into y
480=2x%5E2-16x Distribute
0=2x%5E2-16x-480 Subtract 480 from both sides
Now we use the quadratic formula to solve for x:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-16x%2B-480+=+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=%28-16%29%5E2-4%2A2%2A-480=4096.

Discriminant d=4096 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--16%2B-sqrt%28+4096+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-16%29%2Bsqrt%28+4096+%29%29%2F2%5C2+=+20
x%5B2%5D+=+%28-%28-16%29-sqrt%28+4096+%29%29%2F2%5C2+=+-12

Quadratic expression 2x%5E2%2B-16x%2B-480 can be factored:
2x%5E2%2B-16x%2B-480+=+2%28x-20%29%2A%28x--12%29
Again, the answer is: 20, -12. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-16%2Ax%2B-480+%29


Since a negative width doesn't make any sense, our answer is 20. So our length is
y=2%2820%29-16
y=40-16
y=24
So our width is 20 and our length is 24.