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Izaak and Mylee just bought a house with open land in the backyard. The previous owner left 400 linear feet of fencing. Izaak and Mylee want to construct the fence to give their two dogs the most area possible to play in the backyard.

If they make the length of the fence 80 linear feet or 120 linear feet, the dogs will have a play area of 9,600 square feet. However, if Izaak and Mylee make the length of the fence 100 linear feet, they will be able to create a maximum area of 10,000 square feet.

What is the vertex?

Answer :

The maximum play area will be achieved when the length of the fence is 100 linear feet.

What is Square feet?

Square feet can be defined as the area of a square with sides of 1 foot.

Square feet for their dogs to play in

This situation can be modeled mathematically as follows:

Let's assume that x is the length of the fence in linear feet and y is the area of the play area in square feet.

Based on the given information, we know that:

y = x * (x - 80) (when x = 100)

y = x * (x - 120) (when x = 80 or 120)

Setting these two equations equal to each other, we can find the value of x that results in the maximum play area:

x * (x - 80) = x * (x - 120)

x^2 - 80x = x^2 - 120x

40x = 40 * 100

x = 100

So, the maximum play area will be achieved when the length of the fence is 100 linear feet. The resulting play area will be 10,000 square feet.

Learn more about square feet here: brainly.com/question/16184973

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