SOLUTION: A rectangular playing field with a perimeter of 100 meters is to have an area of at least 500 square meters. Within what bounds must the length of the rectangle lie?

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Question 1057059: A rectangular playing field with a perimeter of 100 meters is to have an area of at least 500 square meters. Within what bounds must the length of the rectangle lie?
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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A rectangular playing field with a perimeter of 100 meters is to have an area of at least 500 square meters.
Within what bounds must the length of the rectangle lie?
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x*(50-x) = 500.    ( Notice that 50 = 100/2 is the half of the perimeter (!)}}}

It is your governing equation.

Simplify and solve it:

x^2 - 50x + 500 = 0,

x%5B1%2C2%5D = %2850+%2B-+sqrt%2850%5E2+-+4%2A500%29%29%2F2 = %2850+%2B-+sqrt%28500%29%29%2F2 = 25+%2B-+5%2Asqrt%285%29%29.


Answer. The length L must lie between 25 and 25+%2B+5%2Asqrt%285%29:  25 <= L <= 25+%2B+5%2Asqrt%285%29. Then the width must be W = 50 - L.