Answer:
1/2 inch
Step-by-step explanation:
The area of a rectangle is the product of its length and width. So, the length and width of the photo will give a product of 24 when they are multiplied together.
One set of factors of 24 is 4 and 6, each of which is 1 unit less than the 5 and 7 dimensions of the paper on which the photo is printed. Hence a 1/2-inch border all around will result in a printed photo that is 4x6 on a 5x7 piece of paper.
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If you want to write and solve equations, you can let b represent the border width. Then the photo area is ...
(5 -2b)(7 -2b) = 24
35 -24b +4b^2 = 24
4b^2 -24b +11 = 0
(2b -1)(2b -11) = 0
Solutions to this quadratic are b = 1/2, b = 11/2. The only viable solution is b = 1/2.
The border is 1/2 inch wide.
