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

Algebra ->  Surface-area -> 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      Log On


   

Question 169537: 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 nerdybill(7384) About Me  (Show Source):
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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?
.
Let w = width of photo
then
w+3 = length of photo
.
If a 2-inch border is added:
width is:
w+2+2 = w+4
.
length is:
w+3+2+2 = w+7
.
(w+4)(w+7) = 108
w^2 + 7w + 4w + 28 = 108
w^2 + 11w + 28 = 108
w^2 + 11w - 80 = 0
.
Factoring we get:
(w+16)(w-5) = 0
w = {5, -16}
.
We can toss out the negative solution so we get:
w = 5 inches (width)
.
Length:
w+3 = 8+3 = 11 inches (length)