Explanation:
To find the width of the border, we first need to calculate the area of the picture.
Area of the picture = length x width = 8 in x 11 in = 88 in²
Let the width of the border be "x".
The new length of the picture will be 11+2x, and the new width will be 8+2x.
The total area of the new picture with the border will be:
total area = (11+2x) x (8+2x) = 108 in²
Expanding this equation gives:
88 + 22x + 16x + 4x² = 108
Simplifying and rearranging the terms, we get:
4x² + 38x - 20 = 0
We can solve for x using the quadratic formula:
x = (-b ± sqrt(b² - 4ac)) / 2a
where a = 4, b = 38, and c = -20.
Plugging in these values, we get:
x = (-38 ± sqrt(38² - 4(4)(-20))) / 2(4)
x = (-38 ± sqrt(1936)) / 8
x = (-38 ± 44) / 8
The two possible solutions are:
x = 1.5 or x = -5
Since a negative width for the border does not make sense, the width of the border should be 1.5 inches.