Ascience museum is going to put an outdoor restaurant along one wall of the museum. the restaurant space will be rectangular. assume the museum would prefer to maximize the area for the restaurant. a. suppose there is 120 feet of fencing available for the three sides that require fencing. how long will the longest side of the restaurant be? b. what is the maximum area?

To maximize the area we want the sides to be as close to similar numbers as possible. For example, a rectangle (40ft x 60ft) shares the same perimeter as a square (50ft x 50ft). The area of the rectangle is 2,400 ft² and the area of the square is 2,500ft². Thus proving that the closer the sides are to being similar numbers, the better chances of maximizing your area.

Now, let's use this information in accordance with the 3 sides having a perimeter of 120ft. Let's find the length of all three sides so that they are equal and add to 120 ft.

120ft ÷ 3sides = 40ft. Each side of the restaurant is 40ft.

The maximum area is 40ft x 40ft.

The answer to A.) is "The longest side of the restaurant is 40ft."
The answer to B.) is "The maximum area of the restaurant is 1,600ft²."

I hope this helps!