Question

A piece of cardboard is 2.5 times as long as it is wide. It is to be made into a box with an open top by cutting 2-inch squares from each comer and folding up the sidesLet x represent the width in inches) of the original piece of cardboard Answer the following questions

Answer 1

The piece of cardboard has dimensions where the length is 2.5 times the width. By cutting 2-inch squares from each corner and folding the sides, you can find the resulting dimensions of the open-top box to calculate its volume.

Step-by-step explanation:

To solve the given problem, we start by letting x represent the width of the cardboard in inches. The length of the cardboard is then 2.5x inches, because it is stated to be 2.5 times as long as it is wide. After cutting 2-inch squares from each corner and folding up the sides to form the open-top box, the new dimensions of the box will be:

• Length: 2.5x - 4 inches (subtracting two times the size of the squares from the original length).
• Width: x - 4 inches (subtracting two times the size of the squares from the original width).
• Height: 2 inches (the size of the squares).

Therefore, the volume of the resulting box can be calculated by multiplying the adjusted length, width, and height.