1. A landscape architect used the entire length of a 75-foot rope to lay out a flower bed in the shape of a square. In another area, he used the entire length of the same rope to lay out a second flowerbed in the shape of a circle. (The drawing below are not to scale.) Perimeter = 75 feet Circumference = 75 feet a. Find the area of each flowerbed. Use 3.14 for. b. Which shape flower bed has the greater area? c. How many square feet greater is the area of the larger flower bed?

a. the area of the square is 351.56 ft ^ 2

the area of the circumference is 447.65 ft ^ 2

b. the circumference has a greater area.

c. 96.02 ft ^ 2

Step-by-step explanation:

We have the following information:

Square perimeter: 75 ft

Circle perimeter: 75 ft

Now we know that the perimeter of the square is:

Ps = 4 * s

we solve for s (side), and we have:

s = Ps / 4, replacing:

s = 75/4

s = 18.75

Now, we can calculate the area of the square, knowing that:

As = s ^ 2

As = 18.75 ^ 2

As = 351.56, therefore the area of the square is 351.56 ft ^ 2

Now we repeat the process for the circle, knowing that the perimeter of the circle is:

Pc = 2 * pi * r

we solve for r:

r = Pc / 2 * pi, replacing:

r = 75 / (2 * 3.14)

r = 11.94

now the circle area is:

Ac = pi * r ^ 2 ^, replacing:

Ac = 3.14 * 11.94 ^ 2

Ac = 447.65, therefore the area of the circumference is 447.65 ft ^ 2

b. The one with the shape of the circumference has a greater area.

c. 447.65 - 351.56 = 96.09

This means that the difference is 96.02 ft ^ 2