Question

A landscape architect used the entire length of an 80-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 flower bed in the shape of a circle. (Drawings not to scale.)
What is the area of the square?



What is the area of the circle? Round your answer to the nearest square foot?



Which shape should the landscape architect recommend to a client who wants the largest possible area for an 80-foot rope?

A.
Square

B.
Circle

Answer 1

Answer: The area of the square is 400sqf.

Answer 2: Area of circle = 509.31 square feet.

Answer 3: The circle because the circle's are is larger

Answer 2

Answers:

• Area of the square = 400 square feet
• Area of the circle = 509 square feet
• Recommended shape with largest area = Circle

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Explanation:

The rope forms the perimeter of each shape. This is the distance around the outer edges.

The square has all four sides the same length. Since we have 80 feet of rope, each side must be 80/4 = 20 feet long.

The area of the square is 20*20 = 400 square feet.

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The circle has a circumference of 80 feet, which leads to a radius of...

C = 2*pi*r

r = C/(2pi)

r = 80/(2pi)

r = 12.732395

which is approximate. I used my calculator's stored version of pi so I could get the most accuracy possible.

Then use this to find the area of the circle

A = pi*r^2

A = pi*(12.732395)^2

A = 509.295782

This value is also approximate.

When rounding to the nearest whole number, we get A = 509

The area of the circle is about 509 square feet.

The circle has the largest area.