Question

2. Sydney wants to create a giant fenced-in playpen for her pets to run around. She decides to place the fence against her house so that she only needs enough fencing for three sides. She has 80 ft of fencing. Note: The diagram is not drawn to scale.

An equation that models the perimeter is P = 2W + L
An equation that models the area is A = (L)(W)
a) Substitute 80 ft into the perimeter equation and isolate one of the variables. [2 marks)

Answer 1

The maximum area of the fenced playpen is 800

How to determine the maximum area of the fenced playpen

From the question, we have the following parameters that can be used in our computation:

Perimeter, P = 80 ft

Also, we have

P = 2W + L

This means that

2W + L = 80

So, we have

L = 80 - 2W

The area is calculated as

A = LW

This gives

A = (80 - 2W)W

Expand

A = 80W - 2W²

Differentiate and set to 0

80 - 4W = 0

So, we have

W = 20

Recall that

A = 80W - 2W²

This gives

A = 80 * 20 - 2 * 20²

Evaluate

A = 800

Hence, the maximum area of the fenced playpen is 800

Question

Sydney wants to create a giant fenced-in playpen for her pets to run around. She decides to place the fence against her house so that she only needs enough fencing for three sides. She has 80 ft of fencing. Note: The diagram is not drawn to scale.

Determine the maximum area of the fenced playpen