Maths Conversion

[BlueToffee]

OK, brain dead today.

Can anybody please help me convert a perimeter of 180 metres into square metres, it's a plot of land.

Thanks in advance.

[sunny-dave]

What shape is the plot?

[BlueToffee]

Rectangular, but not square.

[aelmpvw]

is the shape relevant?

[Prudie]

No unless you tell us the exact length of each side or shape. The area is different even if the perimeter is the same eg 45x45, 70x20, 60x30, 90x1 all have perimeters of 180 but all have different areas.

[BlueToffee]

I don't know, ask sunny-dave

[bibblebub]

the maximum area is when it is a square and is 2025m²

if it is a rectangle the area will be less than that

[boxtops]

if the sides are 60 x 30 m (adding up to 180 all the way round), then it's 1800 square metres - isn't it?

[Prudie]

meant 89x1 but you get my drift..

[sandyRoe]

If it was 50x40 it would have a perimeter of 180 and the area would be 2000 sq mts

[boxtops]

Ah - so the side measurements DO affect the end result, I see what you mean. We can't tell you, then, until you tell us the side measurements.

[BlueToffee]

Didn't realise it was such complicated problem. I'll go back this afternoon and post the four separate lengths early evening, if that will help.

[sunny-dave]

The best shape (for maximum area) would be a circle ... the more 'flattened' the shape gets the smaller the area will become.

[aelmpvw]

i know you're right but my poor brain can't understand how different shapes with the same perimeter can have different square measures

[BlueToffee]

Thank you all for your help so far, stand by.

[boxtops]

nor can I, ael!

[BlueToffee]

Hoping there are still some mathematical brains out there....

[BlueToffee]

Pressed submit too quickly!

The plot in question has lengths of 36m, 46m, 35m and 63m.

[dannyk13]

If you ignore the size of the perimeter, and the plot is rectangular then if you multiply length by breadth in metres you will get square metres.I think.

[Peter Pedant]

BT the length and breadth are relevant -

The most efficient way of enclosing land is - circular
and anything squarish MUST be less - and the least will be pencillish shaped,
almost 90 m long both sides and a few centimetres wide.

so for the circular shape,,,,,,,,,,,,,,,,,,,,180 = 2pr (p is pi and r is radius)
so dividing by 2 ,.............................90 = pr
squaring both sides ..................... 8100 = p2 r 2 ( pi squared r squared )
divide by both sides by pi 8100/p = pr2 (pi r squared)

what does pi r squared remind you of ? exactly the area

so all you have to do is divide 8100 / p which is around 2700

do a check for units ..... m used throughout so the answer is sq m ( or m2)

and there you are - it has to be less than 2700 sq m

cooee bibble bub - I have managed to enclose a bigger area !