Posted by **km** on Thursday, June 28, 2012 at 9:39am.

Mike's family wants to build a rectangular fenced backyard area for their dog. They have a 20-meter length of wire fence and four posts. They can also use the 20-meter straight length of the back of their house as a side of the enclosure, but the fence cannot attach directly to the house. The fence must stretch taught between posts, and they have fasteners to attach the fence to the posts. Describe or sketch a design for the dog enclosure that yields the maximum area using the resources they have. List the dimensions of the enclosure and list the total area. Check your work by describing a similar design that does not enclose as much area.

- algebra -
**Steve**, Thursday, June 28, 2012 at 11:24am
the conditions require that the 4 posts are the corners of the rectangle. So, if the width is x, and the length is along the house, the fence used is x+x+(20-2x)

area = x(20-2x) = 2x(10-x)

the max is achieved when x is midway between the roots, or x=5.

The pen is thus 5x10, with area = 50

suppose the width is 6. The pen is then 6x8 with area = 48

suppose the width is 4. Then the pen is 4x12 with area = 48.

## Answer This Question

## Related Questions

- engineering mathematics 1 - your father wants to fence a rectangular area in ...
- Math - An artist is designing the rectangular wire structure with four ...
- calculus - A dog kennel with four pens is to be constructed. The pens will be ...
- MATH - i need this as quick as possible please Omar is building a straight fence...
- Math - we need to fence off a rectangular section of land in order to make some ...
- Calculus - A fence must be built in a large field to enclose a rectangular area ...
- Math - 1. A gardener has 140 feet of fencing to fence in a rectangular vegetable...
- algebra - A man wants to build a rectangular pen in which to keep his dog. If he...
- math - The diameter of a hydrogen atom is about 5×10^-11 meter. Suppose 8.4×10^8...
- Math - Suppose you have 36 yards of fencing to build a fence around a ...

More Related Questions