SOLUTION: A photo is 3 inches longer that it is wide. A 2-inch border is placed around the photo making the total area of the photo and border 108 square inches. What are the dimensions of t

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Question 169614: A photo is 3 inches longer that it is wide. A 2-inch border is placed around the photo making the total area of the photo and border 108 square inches. What are the dimensions of the photo?
Answer by solver91311(24713) About Me  (Show Source):
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Let the width of just the picture be x, then the length must be x%2B3. If the border is 2 inches wide all the way around, the border must add 4 inches to the overall width and 4 inches to the overall length, so the width with the border must be x%2B4 and the length with the border must be x%2B3%2B4 or x%2B7. Since area is given by length times width, the area of the picture and the border must be %28x%2B4%29%28x%2B7%29 and we know this to be equal to 108 square inches. So:

%28x%2B4%29%28x%2B7%29=108

x%5E2%2B11x%2B28=108

x%5E2%2B11x-80=0

%28x-5%29%28x%2B16%29=0

Therefore, x, the original width of the picture alone, must be either 5 or -16. -16 for a width is absurd and is therefore an extraneous root introduced by the act of squaring the variable. -16 can be discarded and the width of the picture is therefore 5 inches. The length is 3 inches longer, or 8 inches.