Jim wants to build a rectangular parking lot along a busy street but only has 1900 feet of fencing available. If no fencing is required along the street, find the maximum area of the parking lot.

Frances Pham

Frances Pham

Answered question

2022-11-19

Jim wants to build a rectangular parking lot along a busy street but only has 1900 feet of fencing available. If no fencing is required along the street, find the maximum area of the parking lot.

Answer & Explanation

erlent00s

erlent00s

Beginner2022-11-20Added 15 answers

Let the length and width of the rectangular plot be x feet and y feet.
Then we have, 2 ( x + y ) = 1900 x + y = 1900 2 x + y = 950 y = 950 x
If A be the area of the rectangular plot, then we have: A = x ( 950 x ) A = 950 x x 2
For maximum value of A, we must have d A d x = 0 d d x ( 950 x x 2 ) = 0 950 2 x = 0 950 = 2 x x = 950 2 x = 495
Then, the length of the rectangular plot is 495 feet and the width of the rectangular plot is 495 feet.
Now, the area of the rectangular plot is = ( 495 495 ) square feet = 245025 square feet.

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