Answer:
Length (L) ≈ 37.17 inches
Width (W) ≈ 18.58 inches
Height (H) ≈ 0.475 inches
Explanation:
Let's denote the dimensions of the closed box as follows:
Length: L
Width: W
Height: H
We are given the following information:
Volume of the box = 1176 cubic inches
Surface area of the box = 1036 square inches
Length is twice the width (L = 2W)
To find the dimensions, we can set up a system of equations based on the given information and the formulas for volume and surface area of a rectangular box:
Volume (V) of a rectangular box = Length (L) × Width (W) × Height (H)
V = L × W × H
Surface Area (SA) of a rectangular box = 2lw + 2lh + 2wh
SA = 2(LW) + 2(LH) + 2(WH)
Now, let's proceed with the calculations:
Given:
V = 1176 cubic inches
SA = 1036 square inches
L = 2W
Volume equation:
1176 = L × W × H
Surface Area equation:
1036 = 2(LW) + 2(LH) + 2(WH)
Now, substitute L = 2W into the surface area equation:
1036 = 2(2W)(W) + 2(2W)H + 2(W)H
1036 = 4W^2 + 4WH + 2WH
Now, we have two equations:
1176 = 2W^2H
1036 = 6W^2H
Now, we can solve this system of equations to find the values of W and H.
Divide equation 2 by 6:
W^2H = 1036/6
W^2H = 172.67
Now, substitute this value of W^2H into equation 1:
1176 = 2(172.67)
1176 = 345.33
Now, solve for W:
W = √(345.33)
W ≈ 18.58 inches
Now, substitute the value of W into equation 2 to find H:
1036 = 6(18.58)^2H
1036 = 2180.69H
Now, solve for H:
H = 1036 / 2180.69
H ≈ 0.475 inches
Finally, we can find the value of L using the given relationship L = 2W:
L = 2 × 18.58
L ≈ 37.17 inches
So, the possible dimensions of the closed box are approximately:
Length (L) ≈ 37.17 inches
Width (W) ≈ 18.58 inches
Height (H) ≈ 0.475 inches