SOLUTION: A rectangular sheet of paper has an area of 204in. squared. Its dimensions are (x+4) by (x+9). What are the dimensions of the paper. Thank You

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Question 440412: A rectangular sheet of paper has an area of 204in. squared. Its dimensions are (x+4) by (x+9). What are the dimensions of the paper.
Thank You
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
A rectangular sheet of paper has an area of 204in. squared. Its dimensions are (x+4) by (x+9). What are the dimensions of the paper.
.
since area is width times length:
204 = (x+4)(x+9)
FOIL the right:
204 = x^2+9x+4x+36
204 = x^2+13x+36
0 = x^2+13x-170
solve by applying the quadratic formula to get:
x = {8.1, -21.1}
throw out the negative solution leaving:
x = 8.1
.
dimensions are:
12.1 inch by 17.1 inch
.
details of quadratic follows:
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=849 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 8.06880228433347, -21.0688022843335. Here's your graph:
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