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 the area of the parking lot.

  1. 👍
  2. 👎
  3. 👁
  1. Let the length be y ft and the width be x ft.
    (I am looking at 2 widths and 1 length)

    so y + 2x = 1280
    y = 1280-2x

    Area = xy
    = x(1280-2x)
    = - 2x^2 + 1280x

    complete the square ....

    Area = - 2(x^2 - 640x + 102400 - 102400)
    = - (x - 320)^2 + 204800

    so x = 320 , then y = 1280-640 = 640

    the width is 320 ft, and the length is 640 ft

    1. 👍
    2. 👎
  2. 3rd last line should say

    = -2(x - 320)^2 + 204800

    typo at the -2 in front, does not affect the answer.

    1. 👍
    2. 👎
  3. dimensions: 320x640
    max. area 204800

    1. 👍
    2. 👎
  4. ergjoiso;gs;g

    1. 👍
    2. 👎
  5. Where does the 102400 come from

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Geometry

    Jason wants to walk the shortest distance to get from the parking lot to the beach. a.How far is the spot on the beach from the parking lot? b. How far will he have to walk from the parking lot to get to the refreshment stand?

  2. social studies

    1) Suppose that people in your community voted to eliminate all taxes. Which of these goods and services would most likely disappear? a. grocery store parking lots b. regional military base c. neighborhood trash pickup d.

  3. math

    A rectangular lot is bordered on one side by a stream and on the other 3 sides by 600m of fencing. The area is a maximum. Determine the area.

  4. Math

    A rectangular parking lot has an area of 2/3 of a square kilometer. The width is 1/2 of a kilometer. What is the length, in kilometers, of the parking lot?

  1. oblique triangle trigonometry

    A parking lot has the shape of a parallelogram. The lengths of two adjacent sides are 70meters and 100meters. The angle between the two sides is 70o. What is the area of the parking lot?

  2. Statistics

    If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the point in the

  3. algebra

    A rectangular parking lot has a perimeter of 254 inches. The length of the parking lot is 77 inches more than the width. Find the length and the width

  4. math Help!!!!!!

    If Nicholas is located at (-3,2), what is the distance to get to the grocery store? Grocery store is at quadrant 4 and is on 1,-1 A. 2 B. 3 C. 4 D. 5 Is the answer B?

  1. English

    Combine these two simple sentences into one simple sentence with a compound verb. Jenny went to the grocery store. She bought chicken and potatoes. A. Jenny went to the grocery store; she bought chicken and potatoes. B. Jenny went

  2. Business Math

    Abigail sells rice to store. she has a total of 125 cavans that she plans to distribute to three stores. if she gives 1/5 of what she has to store A can she devide the remaining equally to store B and C? how many store A and store

  3. College Algebra

    Jim wants to build a rectangular parking lot along a busy street but only has 2,700 feet of fencing available. If no fencing is required along the‚Äč street, find the maximum area of the parking lot. I got the answer 911.25 which

  4. math

    a rectangular parking lot has a length that is 10 yards greater than the width. the area of the parking lot is 200 square yards.find the length and the width

You can view more similar questions or ask a new question.