Posted by **MathGuru** on Wednesday, January 17, 2007 at 8:38pm.

You have two formulas to use:

A = lw -->area = length times width

P = 2l + 2w -->perimeter

You know the perimeter, which is 200m of fencing.

Let length = x

Now let's solve the perimeter equation for w, using what we know:

200 = 2x + 2w

200 - 2x = 2w

(200 - 2x)/2 = w

2(100 - x)/2 = w

100 - x = w

Therefore:

A = x(100 - x) = 100x - x^2

-x^2 + 100x is the area of the rectangle.

To place the quadratic equation in vertex form, you will need to complete the square:

A = -x^2 + 100x

A = -(x^2 - 100x)

A = -(x^2 - 100x + 2500 - 2500) -->to complete the square, take 1/2 times the middle coefficient and square it (you'll need to add and subtract it as well)

A = -(x - 50)^2 + 2500 -->vertex form

If x = 50, then 100 - x = 50.

To maximize the area, take (50)(50) = 2500 square meters.

I hope this will help with other problems of this type.

Ms. Brown has 200m of fencing with which she intends to construct a rectangular enclosure along a river where no fencing is needed. She plans to divide the enclosure into two parts.

What should be the dimensions of the enclosure if its area is to be a maximum?

Show a complete algebraic solution.

thank you

- mathgebra -
**Whistling**, Friday, October 12, 2007 at 1:45am
blah blah blah

## Answer This Question

## Related Questions

- math,help - help Probblem #6 solve by multiplying through with the common ...
- basic geometric - 10. a rectangle has width the same as a side of a square whose...
- geometric - The perimeter of a rectangular carpet is 70feet. The with is three -...
- algebra - What is the width of a rectangle with a perimeter of 70 feet if its ...
- Math - The perimeter of a rectangle is 34 feet and the area measures 60 square ...
- math - what would the dimensions of a retangle be whose perimeter is 50(P=50)...
- algebra - The perimeter of the state of Wyoming is 1280mi. The width is 90mi ...
- Math - The area of a rectangle is shown below The area of the rectangle is 56 ...
- algebra - 1. What must be added to p to produce q? 2. What is the perimeter of ...
- basic geometry - A rectangle has width the same asa a side of a square whose ...

More Related Questions