a backyard farmer wants to enclose a rectangular space for a new garden within her fenced backyard. She has purchased 120 feet of wire fencing to enclose three sides, and she will use a section of the backyard fence as the fourth side
30 by 60
To find the dimensions of the rectangular space, we can follow these steps:
1. Let's assume the length of the rectangular space to be 'L' and the width to be 'W'.
2. As stated in the question, three sides need to be enclosed with the wire fencing, and the fourth side will be the backyard fence. This means that the total length of the wire fencing used will be the sum of the lengths of the three sides.
3. The perimeter of the rectangular space, excluding the fourth side, can be calculated as: Perimeter = L + W + L = 2L + W.
4. The total length of the wire fencing used is given as 120 feet.
5. Therefore, we can write the equation: 2L + W = 120.
6. Now, we need to consider that the fourth side is already part of the backyard fence. This means that the length of the fourth side is the same as the width of the rectangular space. So, L = W.
7. Substituting L with W in the perimeter equation, we get: 2W + W = 120.
8. Simplifying the equation, we have: 3W = 120.
9. Dividing both sides of the equation by 3, we find: W = 40.
10. Since L = W, L is also 40.
11. Therefore, the rectangular space dimensions are 40 ft x 40 ft.
By following these steps, the backyard farmer can enclose a rectangular garden space with dimensions of 40 feet by 40 feet within her fenced backyard, using 120 feet of wire fencing to enclose three sides.