4 of 44 of 4 Items Question A box shaped like a rectangular prism has a height of 17 in and a volume of 2,720 in³ The length is 4 inches greater than twice the width. What is the width of the box? (1 point) Responses –10 in –10 in 8 in 8 in 20 in 20 in 40 in 40 in Skip to navigation
Let the width be x inches.
The length is 4 inches greater than twice the width, so the length is 2x + 4 inches.
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.
Substitute the given values into the formula:
2720 = (2x + 4)(x)(17)
2720 = 34x^2 + 68x
34x^2 + 68x - 2720 = 0
Divide the entire equation by 2 to simplify it:
17x^2 + 34x - 1360 = 0
Now we can factorize the equation:
17(x^2 + 2x - 80) = 0
17(x + 10)(x - 8) = 0
The possible values for x are -10 and 8. Since the width cannot be negative, the width of the box is 8 inches.