Question

A retail owner business wants to build two adjacent retail stores on a rectangular plot of land. The two stores are marked off on the plot using 154m of tape.Let p represent the total perimeter around the stores marked off by tape. Let A be the are of the rectangular plot of land. Determine the maximum area.

Answer 1

To maximize the area A of a rectangle with a perimeter of 154 meters, the rectangle should be a square with side lengths of 38.5 meters, resulting in a maximum area of 1482.25 square meters.

Step-by-step explanation:

The student is asking how to determine the maximum area of a rectangular plot of land if the total perimeter is 154 meters.

Since the perimeter (p) is the total distance around the boundary of a shape, for a rectangle this can be expressed as p = 2l + 2w, where l is the length and w is the width. Given the perimeter is 154 meters, we have 2l + 2w = 154. Simplifying, we get l + w = 77.

To maximize the area (A) of the rectangle, which is computed as A = l * w, we need to utilize the fact that for a given perimeter, a square has the maximum area. Thus, the rectangle that gives the maximum area would actually be a square with side lengths equal to half the perimeter divided by two. Here that would be 77/2 = 38.5 meters. Therefore, the maximum area would be 38.5 * 38.5 = 1482.25 square meters.