Question

Hassan wants to add a border to a photo he took before he frames it, the final area of the entire framed picture will be 96 square inches, the length of the picture is 10 inches, and the width is 6 inches. What would be the width of the border?

Answer 1

Let x be the border width (in inches). The outer dimensions are 10 + 2x by 6 + 2x, and their area is 96:

(10 + 2x)(6 + 2x) = 96
4x^2 + 32x + 60 = 96
4x^2 + 32x - 36 = 0
x^2 + 8x - 9 = 0

x = [-8 ± √(64 + 36)]/2 = [-8 ± 10]/2 → x = 1 or x = -9 (discard)

So the border is 1 inch wide.