Posted by **Taylor** on Wednesday, February 29, 2012 at 12:51am.

A farmer needs to enclose three sides of a pasture with a fence (the fourth side is a river). The farmer has 42 meters of fence and wants the pasture to have an area of 220 sq-meters. What should the dimensions of the pasture be? (For the purpose of this problem, the width will be the smaller dimension (needing two sides); the length with be the longer dimension (needing one side). Additionally, the length should be as long as possible.)

- Math -
**Steve**, Wednesday, February 29, 2012 at 12:17pm
If the width is w, then the length is 42-2w. So, the area is

y = w(42-2w)

y = -2w^2 + 42w

this is just a parabola, and y reaches its maximum when w = -42/-4 = 10.5

so, the pasture is 10.5 x 21. Area = 220.5

If we want just 220 m^2, then the field is 11x20

## Answer this Question

## Related Questions

- math - A farmer build a fence to enclose a rectangle pasture. He used 190ft of ...
- Applied Math- Gr.11 - A farmer wants to enclose three sides of a rectangular ...
- Algebra 2 - 2. a farmer has 400 meters of fence with which to enclose a portion ...
- math - a farmer has 400 meters of fence with which to enclose a portion of land...
- word problem - a farmer has 800 yards of fencing to enclose a rectangular ...
- Algebra 2 - a farmer has 400 meters of fence with which to enclose a portion of ...
- Algebra 2 - a farmer has 400 meters of fence with which to enclose a portion of ...
- Math - A farmer with 8000 meters of fencing wants to enclose a rectangular plot ...
- Math - farmer wants to enclose his pasture which is bordered by a river. If he ...
- Math (Quadratic Equations) - A field is bound on one side by a river. A farmer ...

More Related Questions