A landscape designer is planning a rectangular patio with an area of 180 square feet. The width of the patio must be 3 feet less than its length $l$. Arrange the following steps in the correct order to model and solve this geometry problem using the strategy described in your course.

A facilities manager is planning a rectangular break area with an area of 180 square feet, where the width must be 3 feet less than the length $l$. The solving process leads to the quadratic equation $l^2 - 3l - 180 = 0$, which yields two mathematical solutions: $l = 15$ and $l = -12$. According to the geometry problem-solving strategy, why is the solution $l = -12$ discarded?

A landscaping contractor is verifying the dimensions for a rectangular stone patio that must have an area of 180 square feet. The design specifications state that the width of the patio must be exactly 3 feet less than its length. According to the geometry problem-solving strategy, the final length of the patio is ____ feet.

A contractor is designing a rectangular patio with an area of 180 square feet. The design specifications require the width of the patio to be 3 feet less than its length $l$. Match each description with the correct mathematical expression or value used in the problem-solving strategy.

A facilities manager is calculating the dimensions for a new rectangular outdoor patio that must have an area of 180 square feet, with a width that is 3 feet less than its length $l$. When applying the geometry problem-solving strategy, substituting the dimensions into the area formula and rearranging the terms produces the standard quadratic equation ${}0 = l^2 - 3l - 180$.

Facilities Planning: Standard Patio Dimensions

Client Proposal: Outlining the Geometry Problem-Solving Strategy for Patio Design