A farmer is enclosing a rectangular area for a pigpen. He wants the length of the pen to be 15 Ft longer then the width. The farmer can only afford no more than 150Ft of fencing. Want is the pen’s greatest possible length?? (((((Solve the problem and SHOW ALL WORK...EXPLAIN in DETAIL, How you got each answer??)))) Thanks so much

Accepted Solution

Let the width = x.
The length is 15 ft more than the width, so the length is x + 15.
The perimeter is less than or equal to 150 ft.

Perimeter formula:
P = 2L + 2W

The perimeter must be less than or equal to 150 ft.
[tex] 2L + 2W \le 150 [/tex]

Now we solve for x, the width.

[tex] 2(x + 15) + 2x \le 150 [/tex]

[tex] 2x + 30 + 2x \le 150 [/tex]

[tex] 4x + 30 \le 150 [/tex]

[tex] 4x \le 120 [/tex]

[tex] x \le 30 [/tex]

x is at most 30 ft.
x is the width.
The length is x + 15, so the length is 30 + 15 = 45.
The length is at most 45 ft.