A college has 1500 feet  of portable rink boards to form three adjacent outdoor ice rinks. Deyermine  the dimensions that will produce the maximum total area od ice surface?

Asked on by maka13

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samhouston | Middle School Teacher | (Level 1) Associate Educator

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A square is the best shape to use to maximize area.  The ice rinks should be set up as 3 adjacent squares.  Let x = the length of the side of one ice rink.  This set up would require 10x:  3 to form the top side, 3 to form the bottom side, 1 to form the left side, 1 to form the right side, and 2 to separate the rinks in the middle.

There are 1500 feet of rink boards.  1500 / 10 = 150.
The dimensions will be as follows:

top:  150 * 3 = 450 feet
bottom:  150 * 3 = 450 feet
left side:  150 feet
right side:  150 feet

This will give a total length of 450 feet and a total width of 150 feet.  (450 + 450 + 150 + 150 = 1200 feet).  The remaining 300 feet will be used as dividers between the rinks, thus using all 1500 feet.

The three square rinks will each have a length and width of 150 feet, thus having an area of 22,500 square feet each.  The total area of the three rinks will be 22,500 * 3 = 67,500 square feet.  This is the same result as total length * total width:  450 * 150 = 67,500 square feet.

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