# What dimensions will produce the greatest area for Sharon's puppy to play, if she purchased 40 feet of fencing to enclose three sides of a fence?

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Using a quadratic to solve this question.

So the length of the side is

So the length of the front is

The maximum area is

#### Explanation:

The wording: **to enclose 3 sides of a fence** implies there is at least one more side.

Assumption: The shape is that of a rectangle.

Set area as

Set length of front as

Set length of side as

Given:

Known:

From

Using

This is a quadratic of general shape

Using the beginnings of completing the square write as:

So the length of the side is

So the length of the front is

The maximum area is

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Describe your changes (optional) 200

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If the shape is a rectangle, the area will be

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The fencing is to be used for

Let the length of each of the shorter sides (the breadth) be

The length will be

For a maximum,

The dimensions will be

If the shape is to be an equilateral triangle:

If the fencing is used to form a semi-circle against a wall, the area will be:

Describe your changes (optional) 200