Question

A farmer has 165 feet of fencing material in which to enclose a rectangular grazing area. He wants the

length x to be greater than 50 feet and the width y to be no more than 20 feet.
write a system of inequalities to represent this situation

Answer 1

2*x + 2*y ≤ 165 ft

x > 50ft

0ft < y ≤ 20ft

Explanation:

For a rectangle with length x and width y, the perimeter of the triangle is:

P = 2*x + 2*y

The perimeter needs to be equal or smaller than the length of fencing that the farmer has, then:

2*x + 2*y ≤ 165 ft

We also know that:

(x strictly larger than 50ft)

x > 50ft

(y can be, at most, 20 ft)

0ft < y ≤ 20ft

(where we added the restriction that y needs to be larger than zero, because we can not have a width equal or smaller than zero)

Then the system of inequalities that represent this situation is:

2*x + 2*y ≤ 165 ft

x > 50ft

0ft < y ≤ 20ft