A rectangular swimming pool is to be built with an area of 1250 square feet. The owner wants 5-foot wide decks along either side and 10-foot wide decks at the two ends. Find the dimensions of the smallest piece of property on which the pool can be built satisfying these conditions.
I have worked the problem out to be Length: 50 and Width: 25. Another answer I got was Length: (125)^1/2 and Width: 1250/(125)^1/2. Apparently these are the wrong answers though. I would really appreciate an explanation of how to do this problem. Thanks.
2007-10-26 16:12:37 · 2 answers · asked by Christian 1 in Science & Mathematics ➔ Mathematics
I set it up exactly like that and ended up with Area = 1450+(12500/W)+20W. When I take the derivative I get (-12500/w^2)+20. When I solve it I get W=25. That gives me the wrong answer which also suggest L=50.
2007-10-26 16:28:56 · update #1
I get the same thing : length of pool = 50 ft, width = 25 ft.
The dimensions of the whole pool, including decking,
would then be : 70 ft x 35 ft.
You didn't state this, so I wasn't sure if you were aware of this.
2007-10-26 18:03:52 · answer #1 · answered by falzoon 7 · 0⤊ 0⤋
Let X and Y be the lengths of the sides of the pool.
Without loss of generality, we can assume that X borders the sides and Y borders the ends -- so the area of the property is
(X+10)*(Y+20)
SInce X*Y = 1250, we have Y = 1250/X
This means that the area of the property is described by:
f(X) = (X+10)*(1250/X+20)
Multiply this out and then take the first derivative. Find where the first derivative is equal to zero. Test to see if this is a minimum.
2007-10-26 23:23:37 · answer #2 · answered by Ranto 7 · 0⤊ 0⤋