math

posted by .

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 -

    blah blah blah

  • mathgebra -

    IM NOTHING

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. algebra

    What is the width of a rectangle with a perimeter of 70 feet if its length is 1 foot?
  2. algebra

    The perimeter of the state of Wyoming is 1280mi. The width is 90mi less than the lenght. Find the width and the length. I don't know what formula to use or how to write it. Perimeter = length + length + width + width = 1280 miles OR …
  3. basic geometric

    10. a rectangle has width the same as a side of a square whose perimeter is 20m. the length of the rectangle is 9m. find the perimeter of this rectangle. 34. The width of a rectangular picture is one-half the length. The perimeter …
  4. basic geometry

    A rectangle has width the same asa a side of a square whose perimeter is 20m.the length of the rectangle is 9m. Find the perimeter of this rectangle. 34. The with of a rectangular picture is on-half the length . The perimeter of the …
  5. geometric

    The perimeter of a rectangular carpet is 70feet. The with is three -fourths the length .Find the width. 38. The length of a rectagular room is six times as the width . The perimeter 84 yards. find the width. 39. The width of a rectangle …
  6. math,help

    help Probblem #6 solve by multiplying through with the common denominator (11)/(3)x + (1)/(6) = (8)/(3)x + (19)/(6) Problem #20 the perimeter of a rectangle is to be no greater than 300in. and the length must be 125in. write an inequality …
  7. math

    what would the dimensions of a retangle be whose perimeter is 50(P=50)inches when the length is 2x-5 ane the width is unknown The width must be 25 - (2x-5) = 30-2x, since the sum of the length and width must be half the perimeter. …
  8. algebra

    1. What must be added to p to produce q? 2. What is the perimeter of the rectangle if the length is 2x-3y and the width is x+2y?
  9. Math

    The perimeter of a rectangle is 34 feet and the area measures 60 square feet. What are the length and width of the rectangle?
  10. Math

    The area of a rectangle is shown below The area of the rectangle is 56 Which of the following are possible values for the length and width of the rectangle?

More Similar Questions