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Help Me With A Very Easy Math Problem  
User currently offlineZweed From Netherlands, joined Apr 2004, 455 posts, RR: 0
Posted (9 years 1 month 1 week 2 days 8 hours ago) and read 1730 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?


Thanks

12 replies: All unread, jump to last
 
User currently offlineWunala From Australia, joined Mar 2005, 949 posts, RR: 0
Reply 1, posted (9 years 1 month 1 week 2 days 8 hours ago) and read 1705 times:

45X20
.
.
.
.
.
.


User currently offlinePetertenthije From Netherlands, joined Jul 2001, 3341 posts, RR: 12
Reply 2, posted (9 years 1 month 1 week 2 days 8 hours ago) and read 1699 times:

30x30 = 120m fence

the 45x20 given by Wunala gives you 130m fence



Attamottamotta!
User currently offlineJan Mogren From Sweden, joined Dec 2000, 2043 posts, RR: 51
Reply 3, posted (9 years 1 month 1 week 2 days 8 hours ago) and read 1696 times:

But 30x30 isn't rectangular.

/JM


36x25 is 122 meters fence

[Edited 2005-06-05 15:14:58]


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User currently offlineAloges From Germany, joined Jan 2006, 8668 posts, RR: 43
Reply 4, posted (9 years 1 month 1 week 2 days 8 hours ago) and read 1685 times:

Quoting Jan Mogren (Reply 3):
But 30x30 isn't rectangular.

Well, it's square - but a square is a rectangle, whereas a rectangle is not necessarily a square.



Walk together, talk together all ye peoples of the earth. Then, and only then, shall ye have peace.
User currently offlinePetertenthije From Netherlands, joined Jul 2001, 3341 posts, RR: 12
Reply 5, posted (9 years 1 month 1 week 2 days 8 hours ago) and read 1685 times:

30,01 x 29,999 = 120 (only very slightly rectangular but still a rectangle)


Attamottamotta!
User currently offlineJan Mogren From Sweden, joined Dec 2000, 2043 posts, RR: 51
Reply 6, posted (9 years 1 month 1 week 2 days 8 hours ago) and read 1675 times:

Way back I was taught that a square is not a rectangle, but never mind.
You are probably correct.

(30,01 x 29,999 = 900,2699 if one wants to argue  Wink )

/JM



AeroPresentation - Airline DVD's filmed in High Definition
User currently offlineKalakaua From United States of America, joined Jan 2004, 1516 posts, RR: 5
Reply 7, posted (9 years 1 month 1 week 2 days 8 hours ago) and read 1670 times:

Sounds like a classic Calc. I problem to me?


Gravity explains the motions of the planets, but it cannot explain who set the planets in motion.
User currently offlineWunala From Australia, joined Mar 2005, 949 posts, RR: 0
Reply 8, posted (9 years 1 month 1 week 2 days 7 hours ago) and read 1648 times:

Quoting Kalakaua (Reply 7):
Sounds like a classic Calc. I problem to me?

And your answer is ??????????????


User currently offlineBackfire From Germany, joined Oct 2006, 0 posts, RR: 0
Reply 9, posted (9 years 1 month 1 week 2 days 7 hours ago) and read 1649 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.


User currently offlineIlikeYYC From United States of America, joined Dec 2003, 1373 posts, RR: 20
Reply 10, posted (9 years 1 month 1 week 2 days 7 hours ago) and read 1640 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.



Fighting Absurdity with Absurdity!
User currently offlineKalakaua From United States of America, joined Jan 2004, 1516 posts, RR: 5
Reply 11, posted (9 years 1 month 1 week 1 day 19 hours ago) and read 1536 times:

Backfire has it... or at least has the jist of it. Other than that, everyone else is wrong!!!


Gravity explains the motions of the planets, but it cannot explain who set the planets in motion.
User currently offlineAirxLiban From Lebanon, joined Oct 2003, 4506 posts, RR: 54
Reply 12, posted (9 years 1 month 1 week 1 day 19 hours ago) and read 1532 times:

ditto Backfire in different terms...

you are minimising Z=2x+2y where xy=900

so x=900/y

so Z=2*(900/y)+2y

Differentiate it...

dZ/dy = 2-1800/y^2

Set it equal to zero, y=30 or y=-30

Since y=-30 does not make sense, we reject that solution and take y=30

Then x=300/y=300/30=30

So you need to go with 30x30.



PARIS, FRANCE...THE BEIRUT OF EUROPE.
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