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)   (Show Source): You can put this solution on YOUR website!
if we let x=width, y=length we get

where the length is

Substitute 2x-16 into y
Distribute
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 (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=4096 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 20, -12. Here's your graph:


Since a negative width doesn't make any sense, our answer is 20. So our length is



So our width is 20 and our length is 24.

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