A farmer is enclosing a rectangular space for a pigpen. He wants the length of the pen to be 15 ft longer than the width. The farmer can afford no more than 150 ft of fencing. What could be the pen’s greatest possible length?
let x--------> the length of the pen y-------> the width of the pen
we know that perimeter of a rectangle=2*[x+y] 2*[x+y] <= 150-------> equation 1 x=y+15-----> y=x-15------> equation 2 substitute equation 2 in equation 1
2*[x+(x-15)] <= 150-----> 2*[2x-15] <= 150-----> 4x <=150+30 4x <= 180 x <= 180/4------------> x <= 45 ft
the answer is the pen’s greatest possible length is 45 ft
