a box shaped like a rectangular prism has a height of 17 inches 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?
A ) -10in
B ) 8in
C ) 20in
D ) 40in
Let's call the width of the box "W".
According to the problem, the length is 4 inches greater than twice the width, so the length can be expressed as 2W + 4.
The volume of a rectangular prism is given by the formula V = length * width * height.
Substituting the given values into the formula, we get:
2,720 = (2W + 4) * W * 17
Dividing both sides of the equation by 17 gives us:
160 = (2W + 4) * W
Expanding the equation, we get:
160 = 2W^2 + 4W
Rearranging the equation to set it equal to 0, we get:
2W^2 + 4W - 160 = 0
Now, we can solve this quadratic equation using factoring or the quadratic formula. Factoring by grouping, we get:
2W^2 + 20W - 16W - 160 = 0
2W(W + 10) - 16(W + 10) = 0
(2W - 16)(W + 10) = 0
Setting each factor equal to zero, we get:
2W - 16 = 0 or W + 10 = 0
Solving these equations, we find:
W = 8 or W = -10
Since width cannot be negative, the width of the box is 8 inches.
Therefore, the correct answer is B) 8 in.