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?
• 3 inches
• 9 inches
• 1 inch
• 4 inches
To find the width of the border, we first need to calculate the area of the actual picture.
Since the length is 10 inches and the width is 6 inches, the area of the picture is:
10 inches * 6 inches = 60 square inches
Now, we know that the final area of the entire framed picture will be 96 square inches. This includes both the picture and the border.
Let x represent the width of the border.
Therefore, the area of the border is:
(10 + 2x)(6 + 2x) - 60 = 96
(10 + 2x)(6 + 2x) - 60 = 96
60 + 20x + 12x + 4x^2 - 60 = 96
4x^2 + 32x = 96
4x^2 + 32x - 96 = 0
x^2 + 8x - 24 = 0
(x + 12)(x - 4) = 0
x = 4 or x = -12
Since width cannot be negative, the width of the border is 4 inches.
Therefore, the correct answer is:
4 inches