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

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

- petertenthije
**Posts:**3345**Joined:**

30x30 = 120m fence

the 45x20 given by Wunala gives you 130m fence

the 45x20 given by Wunala gives you 130m fence

Attamottamotta!

- Jan Mogren
**Posts:**2014**Joined:**

But 30x30 isn't rectangular.

/JM

36x25 is 122 meters fence

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

/JM

36x25 is 122 meters fence

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

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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.

Don't cry because it's over, smile because it happened.

- petertenthije
**Posts:**3345**Joined:**

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

Attamottamotta!

- Jan Mogren
**Posts:**2014**Joined:**

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 )

/JM

You are probably correct.

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

/JM

AeroPresentation - Airline DVD's filmed in High Definition

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.

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.

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.

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!

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.

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.

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.

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