You can put this solution on YOUR website!
First we will find the dimensions of the piece removed.
The formula for the area of a rectangle is:
L * W = 24
L = W + 2
Substitue the value
of L for L
(W + 2) * W = 24
W^2 + 2W = 24
Subtract 24 from each side:
W^2 + 2W - 24 = 24 - 24
Solve the quadratic equation:
W^2 + 2W - 24 = 0
|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=100 is greater than zero. That means that there are two solutions: .
Quadratic expression can be factored:
Again, the answer is: 4, -6.
Here's your graph:
Since -6 isn't a reasonable answer considering our problem, the width
of the inner rectangle
is 4" and the length is 6".
W = 4, L = 6
Since there was 1" margin on all four sides
we add 2" to W and L to get the dimensions of the matting
W + 2 = 6, L + 2 = 8.
The overall dimensions of the matting are 6" wide by 8" long and bob's your uncle!