A gift box has a volume of 450 cubic inches. The width of the box is 4 inches less than the length. The height is twice the width. What is the width in inches of the gift box?
volume = length * width * height, so
w(w+4)(2w) = 450
w = 5
108 cubic inches by 12 inches
Let's assume the length of the gift box is L inches.
Given that the width is 4 inches less than the length, we can write the equation for the width as W = L - 4.
Since the height is twice the width, the equation for the height can be written as H = 2W.
The volume of a rectangular box is calculated by multiplying the length, width, and height. Therefore, the equation for the volume of the gift box can be written as V = L * W * H.
Substituting the values of W and H into the equation for volume, we get:
V = L * (L - 4) * 2(L - 4)
We know that the volume is given as 450 cubic inches, so we can set up the equation:
450 = L * (L - 4) * 2(L - 4)
Simplifying this equation will give us the value for L, which we can then use to find the width. Let's solve it step by step:
Step 1: Expand the expression on the right side of the equation:
450 = L * (L^2 - 4L - 8L + 16)
Step 2: Combine like terms:
450 = L * (L^2 - 12L + 16)
Step 3: Distribute L on the right side of the equation:
450 = L^3 - 12L^2 + 16L
Step 4: Set the equation to zero by subtracting 450 from both sides:
L^3 - 12L^2 + 16L - 450 = 0
To find the value of L, we can either use trial and error or use a numerical method such as Newton-Raphson method or a graphing calculator. Let's use a graphing calculator to find the approximate solution:
By graphing the equation L^3 - 12L^2 + 16L - 450 = 0, we find that the value of L is approximately 10.74.
Now that we have the value of L, we can substitute it back into the equation for the width to find the width of the gift box:
W = L - 4
W = 10.74 - 4
W ≈ 6.74
Therefore, the width of the gift box is approximately 6.74 inches.
To find the width of the gift box, we can use the given information to set up an equation.
Let's assume the length of the box is "L" inches. According to the problem, the width of the box is 4 inches less than the length, so the width would be (L - 4) inches.
Given that the height is twice the width, the height would be 2(L - 4) inches.
The volume of a rectangular box is calculated by multiplying its length, width, and height. So, we can set up the following equation:
Volume = Length × Width × Height
450 cubic inches = L × (L - 4) × 2(L - 4)
Now, we can solve this equation to find the value of "L" (length).