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?
2 Answers
If the shape is a rectangle, the area will be
Explanation:
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:
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