Maths problem. Area of lawn.

[prand]

Please PH maths geniuses. Can you explain something for me?

I measured the perimeter of my dad's lawn (figuring out what size of robo mower to get) which is 87 metres. It's roughly a 35x8.5 metre rectangular shape, so that makes it 297.5 metres squared in area. So, easy, I can get the cheaper mower!

But I was just thinking. If the lawn area was a square, not rectangle shape, but the same perimeter distance of 87m, each side would be an equal 21.75. The area would then be 21.75 × 21.75 which equals 473m2.

Can anyone explain how if the perimeter of a square and rectangle is the same the area is diferrent? It's making me completely doubt my maths abilities, and really, do I need a 600 m2 mower or a 400m2 mower for my dad?!

[darren f]

Perimeter to area ratio. Take an extreme example- area 64m2, as an 8mx8m square- perimeter is 32m. As a 64mx1m rectangle, the perimeter is 130m. This is a principle that comes into play in the construction industry, particularly external wall lengths compared to area when calculated insulation requirements and the like (as a greater external wall length will comparatively ‘leak’ more heat).
So you’ll be fine with the smaller mower!

[mintybiscuit]

Buy a sheep

[anonymous-user]

A square maximises area for any given perimeter length.

Look at it the other way round. You have a square with sides of 10m. Perimeter is 40m, area is 100 sqm.

Now stretch it until it is a rectangle 0.01m x 19.99m. Perimeter is still 40m but the area is 0.1999 sqm.

As the square tends towards a 20m long straight line the area tends to zero.

[bigdog3]

Because 2a + 2b does not equal a x b

And 4a does not equal a^2

Also there is no constant k in these relationships

Dimensions of your "equation" do not balance. LHS has units of length (m) whereas RHS has units of area (m^2). To be valid, dimensions of an equation must balance.

[bigdog3]

mintybiscuit said:

Buy a sheep

Black or white?

[prand]

Great thanks all. That explains a lot! And I can get the smaller (cheaper) mower!

[S6PNJ]

Greg66 said:

A square maximises area for any given perimeter length.

Is it not a circle (and thus circumference) for the greatest area? I do agree with you for a 4 sided shape though.

[bigdog3]

Greg66 said:

A square maximises area for any given perimeter length.

Not quite true

Square with perimeter of 8 metres has an area of 4 square metres.

Circle with perimeter of 8 metres has an area of 5.093 square metres.


For boundary efficiency or least surface area / volume ratio (min heat rejection), circles or spheres are best

[anonymous-user]

I thought it was obvious we were talking about quadrilaterals.

Evidently not.

[bigdog3]

Greg66 said:

I thought it was obvious we were talking about quadrilaterals.

Evidently not.

[anonymous-user]

Cuboids to you, sunshine!

[bigdog3]

Greg66 said:

Cuboids to you, sunshine!

Square sunshine?

[poo at Paul's]

If it was round it would be fking massive?




(I am amazed that this question has been asked!)

[bigdog3]

poo at Paul's said:

(I am amazed that this question has been asked!)

That comment is unfair

Not everyone has a good grasp of maths/physics/science fundamentals. They will have many strengths but these just don't feature strongly. I would wager that the majority of people could not answer the OP's question.

So please don't deter contributors from posting basic questions. They have far more value than most of the crap on this forum