Explanation Given information: A steam pipe must be buried underground to reach from one corner of a rectangular parking lot to the diagonally opposite corner. The dimensions of the parking lot are 500 feet by 800 feet. It cost 5 dollars per foot to lay steam pipe under pavement but only 3 dollars per foot to lay the pipe along one of the long edges of the parking lot. Because of nearby sidewalks , the pipe cannot be laid along the 500-foot sides of the parking lot. : Let the rectangular park be ABCD where AB=800 feet and BC=500 feet and the steam pipe must be buried underground to reach from corner C to corner A .Let steam pipe is laid along the line CE and then along EA , where E is a point on the line AB such that BE= x (in feet) as shown in figure. Then, AE=800-x, Now, triangle EBC is right angled triangle. By Pythagoras theorem, we have E C = ( E B ) 2 + ( B C ) 2 E C = x 2 + ( 500 ) 2 E C = x 2 + 250000 Now, cost of laying steam pipe along EC is $5 per foot and cost of laying steam pipe along EA is $3 per foot

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Chapter 3.4, Problem 59A

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Chapter 3.4, Problem 58A

Chapter 3.4, Problem 60A

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How should the steam pipe be buried so as to cost as little as possible.

Solution Summary: The author explains the cost of laying the steam pipe in a parking lot.

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