Jasmine is manufacturing engineer who is trying to find out if she can use a 12-inch by 12-inch sheet of cardboard and a 15-inch by 16-inch sheet of cardboard to make boxes with the same height and volume. In such a pair of boxes possible?
To determine if Jasmine can use the given sheets of cardboard to make boxes with the same height and volume, we need to compare the dimensions and calculate the volumes of both boxes.
First, let's consider the 12-inch by 12-inch sheet of cardboard. If we use the entire sheet to construct a box, one possible way is to make a square box with equal height, width, and length. So, the dimensions of this box would be 12 inches by 12 inches by 12 inches.
Next, let's examine the 15-inch by 16-inch sheet of cardboard. To construct a box with the same height, width, and length, we need to find the common length that can be used for all three dimensions. Looking at the given dimensions, the greatest common divisor (GCD) of 15 and 16 is 1, which means there is no common length that can be used for all three dimensions while keeping the height the same.
Since there is no common length, Jasmine cannot use the 15-inch by 16-inch sheet of cardboard to construct a box with the same height and volume as the box made from the 12-inch by 12-inch sheet of cardboard.
In summary, it is not possible to create a pair of boxes with the same height and volume using the given sheets of cardboard.