SOLUTION: Can you help me solve this question: 1)George is building a porch wrapped around his whole house. The dimensions of his house are 120m by 160m. If his porch is going to be the same

Question 204672: Can you help me solve this question: 1)George is building a porch wrapped around his whole house. The dimensions of his house are 120m by 160m. If his porch is going to be the same area as his house, how wide will the porch be?

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Can you help me solve this question: 1)George is building a porch wrapped around his whole house. The dimensions of his house are 120m by 160m. If his porch is going to be the same area as his house, how wide will the porch be?
.
Drawing a diagram of the problem will help you "see" how to approach it.
.
Let w = width of porch
then
"area of house" = "area of porch
120 * 160 = [(120+2w)(160+2w)] - (120 * 160)
19200 = [(120+2w)(160+2w)] - 19200
38400 = (120+2w)(160+2w)
38400 = 19200+240w+320w+4w^2
0 = -19200+560w+4w^2
0 = 4w^2+560w-19200
0 = w^2+140w-4800
Solve for w using the quadratic equation we get:
w = {28.489, -168.489}
Toss out the negative solution leaves us with:
w = 28.489 meters
.
Details of quadratic to follow:

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=38800 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 28.488578017961, -168.488578017961. Here's your graph:

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