High School

Madi has 60 linear feet of fencing available to fence her rectangular garden. She does not want to waste any of the fencing, so she will use it all.

1. What does the vertex of the parabola represent in the context of the problem?

2. Suppose Madi wants to ensure that the area of the garden is 216 square feet. What will the dimensions of the garden be?

Answer :

Final answer:

The vertex of the parabola represents the maximum possible area for the garden given limitations of fencing length. To obtain a garden area of 216 sq feet, its dimensions should be 18 feet by 12 feet or vice versa.

Explanation:

The

vertex

of the parabola in this problem would represent the maximum area the garden could have given the constraints of only having 60 linear feet of fencing available. That is because a parabola opens downwards when the problem involves a maximum.

In order to find the dimensions that give Madi an area of 216 sq ft, you would use the formula for the perimeter of a rectangle, which is 2(L+W), where L is length and W is width, and the area formula, which is L x W.

Given the perimeter is 60 feet, and the area is 216 sq ft, you could write these two equations: 2(L+W)=60 and L x W = 216.

Solving these equations, we get two solutions that represent the dimensions of the garden. These are L=18 feet, W=12 feet, or L=12 feet, W=18 feet. Either way, the garden dimensions will ensure an area of 216 square feet.

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