Paul is building a coop for his chickens.

Question

Paul is building a coop for his chickens.He makes sure each chicken has at least 4 square feet of floor space inside the coop.

For each set of dimensions, indicate whether the maximum number of chickens Paul can keep is less that 10, equal to 10, or greater than 10.

Square coop with side length of 10 feet (Less than 10, Equal to 10, Greater than 10)

Rectangular coop with width of 5 feet and perimeter of 26 feet. (Less than 10, Equal to 10, Greater than 10)

Circular coop with diameter of 4 feet. (Less than 10, Equal to 10, Greater than 10)

Answer 1

Hello Dasani

The first thing I would do is make of picture of each coop configuration. You have a square, a rectangle, and a circle.

The next thing is to determine the area of each configuration. Do you know how to do this?

The square coop has an area of A = s x s = 10x10 =100 square feet or ft². If you divide this area by the area for each chicken (4ft²) you will get the number of chickens it can hold. In this case its 100/4 = 25 chickens which is greater than 10.

The rectangle coop is missing the length dimension but you can figure it out. The width is 5 feet and the perimeter is 26 feet. Make a picture. The two lengths have to add up to 16 feet because the other 10 feet of the perimeter adds up to 10 feet. Divide 16 by two because the lengths are equal on a rectangle. The result is 8 feet for the length. The rectangle has a length of 8 and a width of 5 feet. The area then is length times width equals 8 x 5 = 40 ft² Finally dividing by 4 for the number of chickens gives you exactly 10 chickens it can hold.

The circular coop has a diameter of 4 ft. The radius of the circle is one half the diameter and equals 2 ft. The area of a circle formula is A = pi r² If you use 3.14 for the value of pi its fine too. Therefore the area is eqaul to A = 3.14 (2)² which is about 25.13 ft². Finally dividing this by 4 gives you a value slightly over 6. You don't care about the fraction do you? You would need a part of a chicken! So 6 is less than 10.

Answer 2

10 chickens would require 40 sq ft so

a 10 x 10 coop is 100 .... greater than 10

width of 5 with perimeter 26 means length is 8. 8x5 =40 .... equal to 10

diameter 4. Area = pi r^2. Diameter 4 means r =2. A = 3.14 x 2² = 12.64. So less tahn 10