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

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Question 105520This question is from textbook Larson Hostetler Algebra and Trigonomnetry
: A rectangular playing field with a perimeter of 100 meters is to have and area of at least 500 square meters. Within what bounds must the length of the rectangle lie? This question is from textbook Larson Hostetler Algebra and Trigonomnetry

Answer by alvinjohnburgos(11) (Show Source):
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If we represent length and width as L and W, respectively:
The rectangular field must have an area of at least 500sqm (to make it easier, we will use equal sign instead of the greater-than-or-equal sign:
eq1
Perimeter is 100m:
eq2
First, isolate W in eq2:

Then, substitute (50 - L) for W in eq1:

Since L > W:

Since lessening the value of L until 25 makes the area greater: