Question

He can only spend $10 on paint, which is enough to cover 150 ft^2 of surface area. What is the maximum length of the base of the rectangle he can build?

Answer 1

Paint is bought to cover square footage. By looking at length and width, we can get the square footage that will total 150 square feet.

This area can be anything from a square to a long skinny rectangle. The thinner the rectangle, the longer the length.

Example: 10' x 15' = 150 sq.ft.

The longest WHOLE foot would be 150 feet long. This would create a rectangle 150' by 1' = 150 square feet.

I did notice you said surface area, which often is for prisms.