Final answer:
The formula for the volume of a rectangular prism is V = lwh, where l represents the length, w represents the width, and h represents the height.
Step-by-step explanation:
The formula for the volume of a rectangular prism is V = lwh, where l represents the length, w represents the width, and h represents the height. To find the volume, you multiply the length, width, and height together.
In this case, let's represent the height of the box as h. The width of the box is 3 ft longer than the height, so the width can be represented as h + 3 ft. The length is 4 ft longer than the height, so the length can be represented as h + 4 ft. The volume of the box is given as 126 ft³.
Using the formula for volume, we have:
V = (h + 4 ft)(h + 3 ft)(h) = 126 ft³
We can solve this equation to find the value of h and then calculate the width and length from there.