A department store purchases gift boxes that each have a volume of 256 cubic inches. The width of each box is 4 less than the length. The height is twice thw width. What are the dimentions of a gift box?
please!
8 inches x 4 inches x 8 inches
To find the dimensions of the gift box, we need to set up a system of equations based on the given information.
Let's assume the length of the gift box is "x" inches.
The width of the gift box is given as 4 less than the length, so it would be "x - 4" inches.
The height of the gift box is twice the width, so it would be "2 * (x - 4)" inches.
Now, we can calculate the volume of the gift box by multiplying its length, width, and height:
Volume = length × width × height
Given that the volume is 256 cubic inches, we can write the equation as:
256 = x * (x - 4) * 2 * (x - 4)
Now, let's solve this equation to find the value of "x" (the length).
256 = 2x(x - 4)²
256 = 2x(x² - 8x + 16)
256 = 2x³ - 16x² + 32x
Rearranging the equation:
2x³ - 16x² + 32x - 256 = 0
Now, we can find the roots of this equation using factoring, graphing, or numerical methods (like the Newton-Raphson method) to get the value of "x" (the length).
Once we find the value of "x," we can substitute it back into the expressions for width and height to determine the dimensions of the gift box.