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?
• –10 in
• 8 in
• 20 in
• 40 in
17*w*(2w+4) = 2720
2w^2 + 4w = 160
w^2 + 2w + 1 = 80+1 , I completed the square
(w+1)^2 = 81
w+1 = ± √81
w = -1 ± 9
= 8 or some negatiave, which I will reject
the width = 8 inches
Thank you
To find the width of the box, we can solve this problem by setting up an equation based on the given information.
Let's let the width of the box be "x" in inches.
Given that the length of the box is 4 inches greater than twice the width, we can express the length as (2x + 4).
The height of the box is given as 17 inches.
The volume of a rectangular prism is calculated by multiplying the length, width, and height. So we have the equation:
Volume = length * width * height
Plugging in the given values:
2,720 = (2x + 4) * x * 17
Now we can solve this equation to find the width of the box.
Divide both sides of the equation by 17:
160 = (2x + 4) * x
Expand the equation:
160 = 2x^2 + 4x
Rearrange the equation to make it quadratic:
2x^2 + 4x - 160 = 0
Now we can solve this quadratic equation. We can do this by factoring, using the quadratic formula, or by completing the square. Let's factor the equation:
2(x^2 + 2x - 80) = 0
Factor out a 2:
2(x + 10)(x - 8) = 0
Set each factor to zero:
x + 10 = 0 or x - 8 = 0
Solve for x in each equation:
x = -10 or x = 8
Since the width cannot be negative, the width of the box is 8 inches.
Therefore, the correct answer is:
• 8 in