A box shaped like a rectangular prism has a height of 17 in. and a volume of 2,720 in.³. 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.
To solve this problem, we can start by writing the formula for the volume of a rectangular prism:
Volume = length x width x height
Given that the volume is 2,720 in³ and the height is 17 in, we can plug those values into the formula and rewrite it to solve for the length in terms of the width:
2,720 = (2w + 4)w(17)
2,720 = 34w^2 + 68w
34w^2 + 68w - 2,720 = 0
w^2 + 2w - 80 = 0
Now we need to solve this quadratic equation for w. Factoring the equation gives:
(w + 10)(w - 8) = 0
So the possible widths could be 10 in or -8 in. Since the width of the box cannot be negative, the width must be 8 in.
Therefore, the width of the box is 8 in.