Answer: the width of the border is 2 inches.
Step-by-step explanation:
The formula for determining the area of a rectangle is expressed as
Area = length × width
Let x represent the width of the border.
The photo is printed on an 12-inch by 18-inch piece of paper. The width of the photo will be (12 - 2x) inches. The length of the paper will be (18 - 2x) inches.
The area of the paper would be
(18 - 2x)(12 - 2x)
The photo covers 112 square inches and has a uniform border. This means that
(18 - 2x)(12 - 2x) = 112
216 - 36x - 24x + 4x² = 112
4x² - 60x + 216 - 112 = 0
4x² - 60x + 104 = 0
Dividing through by 4, it becomes
x² - 15x + 26 = 0
x² - 13x - 2x + 26 = 0
x(x - 13) - 2(x - 13) = 0
x - 2 = 0 or x - 13 = 0
x = 2 or x = 13
The only possible value for the width of the border is x = 2 inches
