Precalculus/Trigonometry

posted by .

How can I write a polynomial equation for this problem and draw a labeled diagram?

A developer wants to build homes on a rectangular plot of land 4 kilometers long and 3 kilometers wide. In this part of the city, regulations require a greenbelt of uniform width along two adjacent sides. The greenbelt must be 10 times the area of the development. Find the width of the greenbelt.

  • Precalculus/Trigonometry -

    Let the greenbelt width be x. The developed area is (5-x)*(4-x). The greenbelt area is 5x + (4-x)x = 9x - x^2

    The requirement is
    9x - x^2 = 10 *(x^2 -9x +20)
    11 x^2 -99 x +200 = 0
    x^2 - 9x + 200/11 = 0

    The labeled diagram is one rectangle nested inside a larger triangle with one pair of corners aligned, and a gap of x along the two perpendicular opposite sides

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. pre-calculus

    A developer wants to build homes on a rectangular plot of land 4 kilometers long and 3 kilometers wide. In this part of the city, regulations require a greenbelt of uniform width along two adjacent sides. The greenbelt must be 10 times …
  2. math

    Andrea made a car trip of 440 Kilometers. She averaged 54 Kilometers per hour for the frst part of the trip and 80 kilometers per hour for the secound part. If the total trip took 6 hours, how long was she traveling at 80 kilometers …
  3. MATH

    Andrea made a car trip of 440 Kilometers. She averaged 54 Kilometers per hour for the frst part of the trip and 80 kilometers per hour for the secound part. If the total trip took 6 hours, how long was she traveling at 80 kilometers …
  4. Math

    Please help!!! Scott bought 54m of fencing to enclose a rectangular plot of land. The width of the rectangular plot is 12m. Assume Scott uses all the fencing. What is the length of the rectangular plot of land?
  5. Math/Algebra

    Delivery company charges $10 plus 40ยข per kilometer or part of a kilometer. Find the cost for a trip of: a.5 kilometers b.7.5 kilometers c.3.2 kilometers d.Graph the ordered pairs (kilometers, cost). Is this a function?
  6. math problem (please help)

    What are the dimensions of a rectangular tract of land if its perimeter is 70 kilometers and its area is 300 square kilometers?
  7. math

    On a map of scale 1:100 000 a rectangular plot of land measures 7cm by 4cm. what are the actual lengths of the plot in kilometers
  8. math

    A construction crew has just finished building a road. The road is 10 kilometers long. If the crew worked for 4 2/3 days, how many kilometers of road did they build each day?
  9. math

    the distance between new york city and boston is 189.9 miles as the crow flies. how far is it in kilometers?
  10. Algebra

    A farmer wants to divide a rectangular plot into five equal strips using 648 feet of fence. (A) draw a labeled diagram of the plot. (B) find the dimensions of the plot that give the maximum area and the maximum area. (C) state why …

More Similar Questions