Zweed From Netherlands, joined Apr 2004, 455 posts, RR: 0 Posted (9 years 9 months 1 day 14 hours ago) and read 1967 times:

It's sunday afternoon and my girlfriend is taking some math classes, she asked for my help and as I said, its sunday afternoon and I my total lack of math skills is even larger than they would be without this hang over,

A parking lot has the area of 900 sq. metres, it has be rectangular
A fence is going to be built around this lot.
What dimension will give us the least amount of money spent on the fence?

Backfire From Germany, joined Oct 2006, 0 posts, RR: 0
Reply 9, posted (9 years 9 months 1 day 12 hours ago) and read 1886 times:

Assume the parking lot is a rectangle with length x.

Its width must therefore be 900/x

Therefore the perimeter is twice the longer side plus twice the shorter side.

Perimeter P = 2x + 2(900/x)

Therefore P = 2x + 1800/x

From this equation it can be seen that, if x is small, P becomes very high because of the second term. Similarly if x is large, P also becomes high because of the first term. In between there is a value of x for which P becomes a minimum (minimum P, of course, means the shortest fence and the least cost).

To find the minimum of the P-x curve, you have to differentiate P with respect to x:

P = 2x + 1800/x

so: dP/dx = 2 - 1800/(x^2)

The minimum of the P-x curve is the point at which the slope (dP/dx) is zero.

Thus: 2 - 1800/(x^2) = 0

1800 = 2(x^2)

(x^2) = 900

and therefore x = 30

So the length is 30 and the width is (900/x) ... also 30.

It is indeed a square, but since a square is, by definition, rectangular, the problem is solved.

IlikeYYC From United States of America, joined Dec 2003, 1373 posts, RR: 19
Reply 10, posted (9 years 9 months 1 day 12 hours ago) and read 1877 times:

Quoting Petertenthije (Reply 5): 30,01 x 29,999 = 120 (only very slightly rectangular but still a rectangle)

I think that the questions means that it can not be a circle, triangle, pentagon, etc.- it has to have 4 perpendicular sides.

I have been taught that a square is a rectangle- just a special one.