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. Which of the following is the width of the border?(1 point)
Responses

1 inch
1 inch

4 inches
4 inches

3 inches
3 inches

9 inches
9 inches

Answer 1

Let the border width be x. The outer dimensions are (10 + 2x) by (6 + 2x), so

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

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

The border width is 1 inch.