Respuesta :
Answer:
- length: 14 feet , width: 43 feet, or
- length: 86 feet, width: 7 feet
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
- 2x + y = 100
3. The, the area of the fence will be:
- length × width = xy = 600
4. Now you have two equation with two variables which you can solveL
- Solve for y in the first equation: y = 100 - 2x
- Substitute the value of y into the second equation: x (100 - 2x) = 600
5. Solve the last equation by completing squares:
- Distributive property: 100x - 2x² = 600
- Divide both sides by - 1: 2x² - 100x = - 600
- Divide both sides by 2: x² - 50x = -300
- Add the sequare of the half of 50 to both sides: x² - 50x + 625 = 325
- Factor the left side: (x - 25)² = 325
- Square root both sides: x - 25 = ± 18.028
- Clear x: x = 25 ± 18.028
- x = 43.028 ≈ 43 or x = 6.972 ≈ 7
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:
- 43 feet (width) and 14 feet (length), or
- 7 feet (width) and 86 feet (length).
The equations of area and perimeter are xy = 600 and 2x + y = 100. Then the correct option is A.
What is a rectangle?
It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a rectangle, opposite sides are parallel and equal and each angle is 90 degrees. And its diagonals are also equal and intersect at mid-point.
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.
Let x be the length of the backyard and y be the width of the backyard.
She has 100 feet of fencing. Then the perimeter will be
2x + y = P
2x + y = 100
If she needs to enclose a 600 square foot area. Then the area of the rectangle will be
[tex]\rm xy = area\\\\xy = 600[/tex]
Thus, the equations of area and perimeter are xy = 600 and 2x + y = 100. Then the correct option is A.
More about the rectangle link is given below.
https://brainly.com/question/10046743