A box shaped like a rectangular prism has a height of 17 in. and a volume of 2,720 in cubed. The length is 4 inches greater than twice the width. What is the width of the box?
Let's start by determining the width of the box.
Let the width of the box be x inches.
Since the length is 4 inches greater than twice the width, the length is (2x + 4) inches.
Given that the height is 17 inches, the volume of the box can be calculated using the formula:
Volume = Length x Width x Height
Substitute the values into the formula:
2,720 = (2x + 4) * x * 17
2,720 = (34x + 68) * x
2,720 = 34x^2 + 68x
Rearrange the equation to form a quadratic equation:
34x^2 + 68x - 2,720 = 0
Divide the entire equation by 2 to simplify:
17x^2 + 34x - 1,360 = 0
To solve for x, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 17, b = 34, c = -1,360
Plugging the values into the formula:
x = (-34 ± sqrt(34^2 - 4*17*(-1,360))) / 2*17
x = (-34 ± sqrt(1,156 + 92,320)) / 34
x = (-34 ± sqrt(93,476)) / 34
x = (-34 ± 305.7) / 34
x = (-34 + 305.7) / 34 or x = (-34 - 305.7) / 34
x = 271.7 / 34 or x = -339.7 / 34
x ≈ 7.992 or x ≈ -9.988
Since the width cannot be negative, the width of the box is approximately 7.992 inches.