Pre-Calc

One campus of HCC has plans to construct rectangular parking lot on land bordered on one side by a highway. There are 640 ft of fencing available to fence the other sides. Let x represent the length of each of the two parallel sides of fencing.

a. draw the illustration of the problem
b.express length of remaining side to be fenced in terms of x.
c. what're the restrictions on x?
d. Determine values of x that'll give area between 30,000 and 40,000 ft squared.
e. what dimensions will give a max area, and what will this area be?
f. Determine a function A that represents the area of the parking lot in terms of x.

  1. 👍 0
  2. 👎 0
  3. 👁 133
asked by Andy G
  1. a) --- up to you
    let the length of the side which is parallel to the highway be x , x < 640
    let the length of the other two equal sides by y each
    x + 2y = 640 ---> y = (640-x)/2 = 320 - x/2

    area = xy = x(320-x/2)
    = 320x - (1/2)x^2

    so we need the vertex of this downwards opening parabola
    the x of the vertex = -b/(2a) = -320/(-1) = 320

    if x = 320, then y = (640-320)/2 = 160

    and the maximum area is (160)(320) = 51200 ft^2

    for part d)
    30000 = 320x - x^2/2
    x^2 - 640x + 60000 = 0
    x = (640 ± √169600)/2 = 114.1 ft or 529 ft
    if x = 114.1 then y = 262.95 and area = 30003

    if x = 529 ft then y = negative, no way

    40,000 = 320x - x^2/2
    x^2 -640x + 80000 = 0
    x = 170.33 , then y = 234.83 ft, area = 39998.6

    I will leave it up to you to split up my solutions into the individual parts b), c) etc

    1. 👍 0
    2. 👎 0
    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. pre-cal

    One campus of Houston community college has plans to construct a rectangular parking lot on land bordered on one side by a highway. there are 640 feet of fencing available to fence the sides. let x represent the length of each off

    asked by Jeremy on February 23, 2015
  2. pre- calc

    area of a parking lot: One campus of Houston community college has plans to construct a rectangular parking lot on land bordered on one side by a highway. there are 640 feet of fencing available to fence the sides. let x represent

    asked by steph on November 10, 2011
  3. algebra

    a local grocery store has plans to construct a rectangular parking lot that is bordered on one side by a highway. there are 1280 feet of fencing avaliable to enclose the other three sides. find the dimensions that will maximize

    asked by Anonymous on November 30, 2010
  4. College Algebra

    The campus of a college has plans to construct a rectangular parking lot on land bordered on one side by a highway. There are 720 feet of fencing available to fence the other three sides. Let x represent the length of each of the

    asked by Cameron on October 15, 2012
  5. Algebra

    A community college campus plans to construct a rectangular parking lot on land bordered on one side by a highway. There are 640 feet of fencing available to fend the other three sides. Let x represent the length of each of the

    asked by Shannon on November 26, 2014
  6. Calculus

    a college is planning to construct a new parking lot. the parking lot must be rectangular and enclose 6000 square meters of land. A fence will surround the parking lot, and another fence parallel to one of the sides will divide

    asked by Marc on November 26, 2010
  7. Calculus

    a college is planning to construct a new parking lot. the parking lot must be rectangular and enclose 6000 square meters of land. A fence will surround the parking lot, and another fence parallel to one of the sides will divide

    asked by Oswaldo on November 26, 2010
  8. math

    Houston Community College is planning to construct a rectangular parking lot on land bordered on one side by a highway. The plan is to use 640 ft of fencing to fence off the other three sides. What should the dimensions of the lot

    asked by Ashley on April 14, 2014
  9. math

    Palo Alto College is planning to construct a rectangular parking lot on land bordered on one side by a highway. The plan is to use 560 feet of fencing to fence off the other three sides. What dimensions should the lot have if the

    asked by James on March 5, 2018
  10. algebra

    A college is planning to construct a rectangular parking lot on land bordered on one side by a highway. The plan is to use 520 feet of fencing to fence off the other three sides. width length

    asked by mm on February 7, 2016

More Similar Questions