a square and a bigger square

shahar

shahar

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I have a side of square that denoted by x.
I have also an other square that his side is (x + m).
I want to show that the area of (x+m)-square bigger If m > 0 from the x-square.
How can I prove it?
 
shahar said:
I have a side of square that denoted by x.
I have also an other square that his side is (x + m).
I want to show that the area of (x+m)-square bigger If m > 0 from the x-square.
How can I prove it?
Click to expand...
What is the expression for the area of a square with side 'x'?

What is the expression for the area of a square with side 'x+m'?
 
shahar said:
I have a side of square that denoted by x.
I have also an other square that his side is (x + m).
I want to show that the area of (x+m)-square bigger If m > 0 from the x-square.
How can I prove it?
Click to expand...
Substitution is one way to prove it.
 
O.K.
I look at my question and I need to go deeper. (I didn't notice that I ask the question that I want to ask).
I have 2 squares one has side that is x and the another has side is that x+m.
If m > 0 then how I justified that the bigger square is with side x+m? How can I prove it? What assumptions I need to write so I can say for sure that x is of the smaller square?
[Sorry about that I don't ask the correct question (that I want to ask).]
 
Questions about proof are hard to answer because we do not know what you are allowed to use as axioms and theorems.

But if you are allowed to use as axioms or theorems

[math]a > 0 \implies a + b > b \text { and }\\ p > 0 \text { and } q > r \implies pq > pr[/math]
the proof is trivial.
 
Subhotosh Khan said:
You are not thinking!

How do you prove "some number" is bigger than another number?
Click to expand...
I see that by subscription, As Jeff wrote.
I see that if A is bigger than B there is operation that call adding that by this operation I can show that A = B + amount.

What am I asking for: I have a paper with 2 squares. One is bigger than the other. How can I denote the notion x and x+m (m > 0) to each square?
 
shahar said:
What am I asking for: I have a paper with 2 squares. One is bigger than the other. How can I denote the notion x and x+m (m > 0) to each square?
Click to expand...
As m > 0, (x+m)-x is positive. Which means (x+m) > x
Therefore, (x+m) denotes a side of the bigger square and x denotes a side of smaller square.
 
shahar said:
O.K.
I look at my question and I need to go deeper. (I didn't notice that I ask the question that I want to ask).
I have 2 squares one has side that is x and the another has side is that x+m.
If m > 0 then how I justified that the bigger square is with side x+m? How can I prove it? What assumptions I need to write so I can say for sure that x is of the smaller square?
[Sorry about that I don't ask the correct question (that I want to ask).]
Click to expand...
What level of work are you doing here? You posted this under Geometry so I would presume that if m > 0 we may simply state that x + m > x. If you need more:
1) m > 0 by the problem statement

2) x= x by reflexivity

3) Thus m + x > 0 + x by the additive law

4 ) m + x > x

That line of reasoning should be sufficient for anything in Geometry.

-Dan
 
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