SOLUTION: A rectangular playing field with a perimeter of 120 meters is to have an area of at least 500 square meters. Within what bounds must the length of the rectangle lie (in meters)? (R

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Question 958510: A rectangular playing field with a perimeter of 120 meters is to have an area of at least 500 square meters. Within what bounds must the length of the rectangle lie (in meters)? (Round your answers to one decimal place. Enter your answer using interval notation.)

I did p=2l+2w=120
w=60-l
A=l.w>500
-l^2+60l-500>0
x= 50,10
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
A couple of those steps look strange, and your variable choice is confusing.

w and L for the dimensions.
system%282L%2B2w=120%2C+wL%3E=500%29;
What can you do with that system?

L%2Bw=60
w=60-L
Now, your shown steps make more sense.
Substitution:
%2860-L%29L%3E=500
60L-L%5E2-500%3E=0
-60L%2BL%5E2%2B500%3C=0
L%5E2-60L%2B500%3C=0, which comes from a parabola opening upward, the minimum below the horizontal axis, and you are interested in the part between the two real roots.

Discriminant, 3600-4%2A500=3600-2000=1600.
L=%2860%2B-+sqrt%281600%29%29%2F2
L=%2860%2B-+40%29%2F2
Taking as large as possible, this length can be between roots 10 and 50.

Interval Notation for your answer,
[10,50].