A box shaped like a rectangular prism has a height of 17 in. and a volume of 2720 in^3. The length is 4 inches greater than twice the width. What is the width of the box?
Please solve and explain what I need to do. The choices are:
-10
8
20
40
Volume of rect. prism = area of base * height
x = width of base of prism
2x + 4 = length of prism base
2720 = x(2x + 4) * 17
To find the width of the box, we can start by thinking about the formula for the volume of a rectangular prism:
Volume = Length x Width x Height
In this case, we are given that the volume of the box is 2720 in^3 and the height is 17 in. So we have:
2720 = Length x Width x 17
Next, we are given that the length is 4 inches greater than twice the width. Let's say the width is represented by "w". Then the length would be 2w + 4. So we can substitute this expression into the equation:
2720 = (2w + 4) x w x 17
Now, we can solve for the width. First, let's simplify the equation:
2720 = 34w^2 + 68w
Rearranging the equation to set it equal to zero:
34w^2 + 68w - 2720 = 0
Next, we can divide the equation by 34 to simplify it further:
w^2 + 2w - 80 = 0
Now, we can solve this quadratic equation for w. We can factor it, use the quadratic formula, or complete the square to find the roots. In this case, we can factor it:
(w + 10)(w - 8) = 0
From this, we can see that the possible values for the width are -10 and 8. However, the width cannot be negative, so the only valid solution is w = 8.
Therefore, the width of the box is 8 inches.