A box shaped like a rectangular prism has a height of 17 in and the volume 2720 in.² is the length of 4 inches greater than it twice of the width. What is the width of the box?
Let x be the width of the box.
The length of the box is 2x + 4.
The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
Given that the height is 17 in and the volume is 2720 in.², we have:
2720 = (2x + 4)(x)(17)
2720 = 34x^2 + 68x
34x^2 + 68x - 2720 = 0.
Divide the entire equation by 2:
17x^2 + 34x - 1360 = 0.
Factorize the quadratic equation:
(17x - 40)(x + 34) = 0.
Setting each factor to zero gives:
17x - 40 = 0
17x = 40
x = 40 / 17
x ≈ 2.353
OR
x + 34 = 0
x = -34
Since the width cannot be negative, x = 2.353.
Therefore, the width of the box is approximately 2.353 inches.