Question

PLSSS HELP AND PLEASE SHOW WORK ASWELL

Collin has 100 feet of fencing to enclose a pen for his puppy. He is
trying to decide whether to make the pen
circular or square. He plans to use all of the
fencing.

Part A.) If Collin uses all of the fencing, what
would be the area of each pen? Use 3.14
for pie. Round to the nearest hundredth if
necessary.

Part B.) To have the largest possible area for the pen, which pen should Collin build?

Answer 1

Part A:

Let's first consider the circular pen. The circumference of a circle is given by 2πr, where r is the radius. In this case, we have 100 feet of fencing, so:

2πr = 100

Solving for r, we get:

r = 100/(2π) = 15.92 feet (rounded to two decimal places)

The area of the circular pen is given by πr^2, so:

Area = π(15.92)^2 = 795.77 square feet (rounded to two decimal places)

Now let's consider the square pen. If we use all 100 feet of fencing, then each side of the square will be 25 feet long. Therefore, the area of the square pen is:

Area = 25^2 = 625 square feet

Part B:

To have the largest possible area for the pen, Collin should build the circular pen. We can see from the calculations above that the area of the circular pen is larger than the area of the square pen. This is because a circle has the largest area for a given perimeter, which in this case is 100 feet.

Answer 2

A.

circular: ≈ 795.77 square feet

square: 625

Explanation:

the circular pen would have a larger area.

Solving for the radius, we have:

r = 100 / (2 × 3.14) = 15.92 feet (rounded to two decimal places)

Therefore, the area of the circular pen would be:

Area = πr^2 = 3.14 × (15.92 ft)^2 ≈ 795.77 square feet

For a square pen with side length s, the perimeter is given by:

4s = 100

s = 25

The area of a square pen with side length s is given by:

A = s^2 = 25^2 = 625