An open box is made by removing squares of length x in each corner of 8 unit by 6 unit rectangular piece ofcardboard. HOw long is × so that the volume of the resulting box is 192unit.
base will be 8-2x by 6-2x
height = x
volume = x(8-2x)(6-2x) = 192 , where x<3
x(48 - 28x + 4x^2 = 192
4x^3 - 28x^2 + 48x - 192 = 0
x^3 - 7x^2 + 12x - 48 = 0
tried all the "nice" factors of 48, and found no solution.
So I let Wolfram graph it and solve it to ge
x = appr 6.3
but that would make the length and width turn out to be negative numbers,
your problem has no solution.
To find the length of x, we need to understand the dimensions of the resulting box after removing squares from the corners.
Let's visualize the problem:
We have a rectangular piece of cardboard with dimensions 8 units by 6 units.
We remove squares of length x from each corner of the rectangle.
Then we fold up the flaps to form the box.
Since the length of the resulting box is not mentioned, let's assume that the length of the box is L units.
The width of the box will be the remaining width of the rectangle after removing the squares from the corners. This can be calculated as (6 - 2x) units.
Similarly, the height of the box will be the remaining height of the rectangle after removing the squares from the corners. This can be calculated as (8 - 2x) units.
Therefore, the volume of the resulting box can be calculated as V = L * (6 - 2x) * (8 - 2x).
According to the problem, we know that the volume of the resulting box is 192 units.
So we can set up the equation:
192 = L * (6 - 2x) * (8 - 2x)
Now, we need to solve this equation to find the value of x.
To do that, we can rearrange the equation to get it in standard form:
192 = (6 - 2x) * (8 - 2x) * L
Now, we can simplify the equation by expanding the brackets:
192 = (48 - 28x + 4x^2) * L
Rearranging the equation again gives:
4x^2 - 28x + 48 = 192 / L
Now, the problem does not provide the value of L, so we cannot solve for x directly. However, if you have a specific value for L, you can substitute it and solve for x.
You can then use the value of x obtained to determine the value of L, by substituting it back into the equation or using trial and error until the volume of the resulting box is 192 units.