A farmer has 165 feet of fencing material in which to emclose a rectangle area. He wants the length x to be greater than 50 feet and width y to be no more than 20 feet. write a system to represent this situation.
To represent this situation, we can use the following system of inequalities:
1. The perimeter of the rectangle must be equal to the available fencing material: 2(x + y) = 165.
This equation represents the fact that the total length of the four sides of the rectangle (2 times the sum of the length and width) is equal to the given amount of fencing material.
2. The length of the rectangle should be greater than 50 feet: x > 50.
This inequality ensures that the length (x) of the rectangle is greater than 50 feet.
3. The width of the rectangle should be no more than 20 feet: y ≤ 20.
This inequality ensures that the width (y) of the rectangle is less than or equal to 20 feet.
By combining these three equations, we can represent the given situation mathematically.