SOLUTION: A rectangular piece of picture matting is 2 inches longer than it is wide. A rectangular region is cut out of the middle for a picture, leaving 1 inch of matting all around. If the

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Question 282144: A rectangular piece of picture matting is 2 inches longer than it is wide. A rectangular region is cut out of the middle for a picture, leaving 1 inch of matting all around. If the area of the region that is removed is 24 square inches, what are the dimensions of the matting?
Answer by Deina(147)   (Show Source): 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

Expand:
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!
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