Question

Matt and his dad are building a tree house. They buy enough flooring material to cover an area of 36 square ft. What are all possible dimensions of the floor?

Answer 1

Factor pairs of 36 are ...

1×36, 2×18, 3×12, 4×9, 6×6 . . . and the reverse of these

There is nothing in the problem statement limiting the dimensions to integer numbers of feet, so any dimensions x and 36/x will do. (x in feet)

Explanation:

Area is the product of length and width. The desired dimensions are the length and width of the floor, so any pair of numbers resulting in a product of 36 will be a possible set of dimensions.

If the dimensions are supposed to be integer numbers of feet, then the possibilities for length×width are ...

1×36, 2×18, 3×12, 4×9, 6×6, 9×4, 12×3, 18×2, 36×1

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As a practical matter, the tree house probably needs to be wider than 2 feet, leaving 3×12, 4×9, and 6×6 as possible dimensions (length×width or width×length). Depending on the flooring material and the difficulty of cutting it, there may be other limitations on the dimensions.