# AreaWatch

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#1
I'm confused!

An area is x unit . x units and the result is x2.

So, how come that the solution of an exercise:

1 x (3x +2 +sqrt5x) = (3x +2 +sqrt5x)

(1 being the measurement of one side of a rectangle, and the other expression in brackets the other side; no units are given)

and NOT as I maintain (3x +2 +sqrt5x)2 ?
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5 years ago
#2
(Original post by Jorge)
I'm confused!

An area is x unit . x units and the result is x2.

So, how come that the solution of an exercise:

1 x (3x +2 +sqrt5x) = (3x +2 +sqrt5x)

(1 being the measurement of one side of a rectangle, and the other expression in brackets the other side; no units are given)

and NOT as I maintain (3x +2 +sqrt5x)2 ?
Because a rectangle isn't a square!

Rectangle area = width x height.

You have a width of 1 and the height is other ugly expression involving x. So the area is just ...
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#3
(Original post by davros)
Because a rectangle isn't a square!

Rectangle area = width x height.

You have a width of 1 and the height is other ugly expression involving x. So the area is just ...

Not to the square?

a line is linear
a 3D objedt is to the cube

Surely any surface (area( has to be to the square whatever units you use.

i would be grateful if you couldd explain in full your reasoning.
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5 years ago
#4
(Original post by Jorge)
Not to the square?

a line is linear
a 3D objedt is to the cube

Surely any surface (area( has to be to the square whatever units you use.

i would be grateful if you couldd explain in full your reasoning.
I've given you the formula:

area = width x height

If your sides were 1 unit and 6 units then the area is , not

If your sides were 1 unit and x units then the area is , not

If your sides were 1 unit and then the area is , not

Simply apply the same reasoning to your example.
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5 years ago
#5
(Original post by Jorge)
Not to the square?

a line is linear
a 3D objedt is to the cube

Surely any surface (area( has to be to the square whatever units you use.

i would be grateful if you couldd explain in full your reasoning.
The units would be squared

cm^2 or m^2 or whatever

But, as you point out there are no units mentioned in this question
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#6
Hi

We are talking about different things... and it's probably my fault.

of course 6x 6 = 36 but if it an area it is 36 something2 whether it is meters, cm, or broom handles.
In this case they give no units but the result has to be to something (no unites) squared

The fact that we are talking about an area forces the result to have units2 even if the problem does not mention them.

So, the next question is how should that be stated amthematically?

Maybe (3x +2 +sqrt5x)u2
with a note u=units

But, YES, I was wrong... although the "right" result with no indication of units squared is also wring, as far as I am concerned.
0
5 years ago
#7
(Original post by Jorge)
Hi

We are talking about different things... and it's probably my fault.

of course 6x 6 = 36 but if it an area it is 36 something2 whether it is meters, cm, or broom handles.
In this case they give no units but the result has to be to something (no unites) squared

The fact that we are talking about an area forces the result to have units2 even if the problem does not mention them.

So, the next question is how should that be stated amthematically?

Maybe (3x +2 +sqrt5x)u2
with a note u=units

But, YES, I was wrong... although the "right" result with no indication of units squared is also wring, as far as I am concerned.
You are writing an expression you do not need a unit
0
#8
(Original post by TenOfThem)
You are writing an expression you do not need a unit
That's where I disagree. This was not just expressions put together, They were the sides of a rectangle and the question asked for the area. An area must always bt to the square of the unit, even if imaginary. No units: no area!
0
5 years ago
#9
(Original post by Jorge)
That's where I disagree. This was not just expressions put together, They were the sides of a rectangle and the question asked for the area. An area must always bt to the square of the unit, even if imaginary. No units: no area!
There's nothing wrong with the answer. If no units are specified then the units are taken to be either irrelevant or implicit.

So if you have a side of 4cm and a side of 5cm then the area should be quoted as 20cm^2,

But if the sides are given as 4 and 5 and no units are given, then it is implicit that both linear dimensions have the same units and the area is just 20 (with the implication that this refers to squared units of the corresponding linear measure),

There's no need to add extra symbols to the result because everyone understands this convention
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#10
(Original post by davros)

everyone understands this convention
I will let the matter rest, but I am from the times when maths were considered an exact science, and not subject to conventions.

Interesting discussion, though.

Many thanks, all.
0
5 years ago
#11
(Original post by Jorge)
I will let the matter rest, but I am from the times when maths were considered an exact science, and not subject to conventions.

Interesting discussion, though.

Many thanks, all.
Your first post correctly identified that a square with side x would have an area of x^2

There is no requirement to put units^2 after this

If you were asked for rule for the area of a triangle you would say 1/2 bh

You would not say units^2
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#12
(Original post by TenOfThem)

If you were asked for rule for the area of a triangle you would say 1/2 bh

You would not say units^2

I take your point, but one thing is a formula to be used for cm, m, km , inched or whatever; the other is a definite area. If units are no longer required mathematics has become rather sloppy!

Time to go to bed here!

Good night and thank you for the entertainment.
0
5 years ago
#13
(Original post by Jorge)
I take your point, but one thing is a formula to be used for cm, m, km , inched or whatever; the other is a definite area. If units are no longer required mathematics has become rather sloppy!

Time to go to bed here!

Good night and thank you for the entertainment.
I disagree

When area is seen as something concrete - the space inside a 2D shape - with a value - then units are relevant

When we extend the concept into the abstract - use algebra to give general expressions - the units are not relevant

Let me ask you this - if you were finding the area under a curve what units would you insist on - what if the curve were showing speed against time
0
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