A piece of cardboard has a length of 60cm and a width of 40cm. In order to make the cardboard into an open box, a box with no lid), a piece of length x must be cut out of each corner.
Write an equation to represent each dimension of the box.
To represent each dimension of the open box, we need to subtract 2x from the length and width of the cardboard. Here are the equations:
Length of the box: 60cm - 2x
Width of the box: 40cm - 2x
To find the dimensions of the box, we need to consider the length, width, and height.
1. Length of the box:
When we cut out the corners of length x from the original cardboard, it will reduce the length by 2x (as we are removing x from each end). So, the length of the box will be: 60cm - 2x.
2. Width of the box:
Similar to the length, cutting out the corners of length x will reduce the width by 2x. So, the width of the box will be: 40cm - 2x.
3. Height of the box:
The height of the box will be the length of the cut-outs taken from each corner. So, the height will be: x.
Therefore, the dimensions of the box can be represented by the equation:
Length = 60cm - 2x
Width = 40cm - 2x
Height = x
From each side, the cut at each end is x, so the length and width left is 60-2x and 40-2x respectively.
The height, when the sides are folded, is x.