# 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?

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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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