Gabi is working on another backyard project. she is building a fence to keep deer out of her garden. one side of her garden is against a wall, so she only needs to build three sides of the fence. she has 100 feet of fencing. if she needs to enclose a 600 square foot area, what should the length and width of her fence be? xy = 600 2x + y = 100 y = -2x x(-2x + 100) = x x = 600 x2 – 50x = -300 (x – 25)2 = 325 |x – 25| = 5

Both solutions are valid.

Explanation:

1. First assumption is that the shape of the fence is rectangular.

2. Second, assum the length parallel to the wall measure y feet, so the other two lengths, y, together with x will add up 100 feet

3. The, the area of the fence will be:

4. Now you have two equation with two variables which you can solveL

5. Solve the last equation by completing squares:

Both values are valid,

If x = 43 , then y = 600/43 = 14

If x = 7, then y = 600/7 = 86

Thus, the lenght and width of the fence may be:

step-by-step explanation:

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