Question

Could you please help me with question?
@mathmate
@dumbcow
@SolomonZelman

Answer 1

To help you get your answer faster, I suggest you post your question before tagging for help! :)

Answer 2

I think it's Statement 6.
@mathmate Sorry, usually everyone takes forever to come.

Answer 3

These are the answer choices:

A. Statement 4
B. Statement 5
C. State... 6
D. Statem.. 7

Answer 4

They ask which is the \(first\) incorrect statement.
This type of question is best answered by examining each statement in order, and be convinced that each one you looked at is correct before moving to the next one.
This is a very good training in mathematical reasoning, so do not miss the chance of practice.
If you tell me statement 6 is incorrect, you need to tell me first that statements 1,2,3,4,5 are ALL correct. Are you ready to make that claim?

Answer 5

I don't know how to explain it, I know figure B has 2x's and 2y's shaded,figure = x^2 +y^2 + 2xy so I choose statement 6.
@mathmate
However, I did ask for help because I don't really understand too much of this problem.

Answer 6

To do it properly, as I explained above, you need to
Start with statement 1.
Is statement 1 correct, and why?

Answer 7

There are four triangles shaded and divided by halves, 2 triangles on the x side and 2 on the y side, which results in 2xy. Yes, it is correct.

Answer 8

Very good! Especially the explanation.
Now can you proceed the same way with statement 2?

Answer 9

Aww, thanks!
I'm trying to figure 2 out, but I'm not too sure. 4 half triangles are equivalent to c^2 ?

Answer 10

Yes, you could say the white square has side =c, so area is c^2,
Or, along the lines of your argument, there are 4 isosceles right triangles with hypotenuse c, so each leg is sqrt(c)/2, total area
= 4((sqrt(c)/2)^2)=c^2.

Good, can you proceed to statement 3?

Answer 11

Statement 3 sums up the end result of both Statement 1 and 2,
in Statement 1 I've proved 2xy is the end result and as stated above in statement 2- we concluded figure A= c^2. In order to find the area of figure A, you would add both of these which combines the end result of Statement 1 and 2 .

Answer 12

Absolutely correct!

You can now continue with statement 4.

Answer 13

Therefore, we would add c^2 and 2xy= area.
Statement 4: there are 4 squares which are divided by both x and y.
4 / 1/2 = 2 and if you include the variables it's 2xy

(I'm not sure how much sense that mad.. )

Answer 14

that made*

Answer 15

Not exactly.
The four grey triangles together have the same area as the two grey rectangles.
Each grey rectangle has an area of a\(\times\)b, or x\(\times\)y or xy.
So two rectangles together have an area of 2xy, so the statement is still correct.
You follow so far?

Answer 16

YEs.

Answer 17

Now let's move on to #5.
If you find #5 valid, then your proposed answer of #6 is correct (i.e. #6 is not valid).
If #5 is not valid, then your answer should be #5 (first invalid statement)
You follow the logic?

Answer 18

@lilia222

Answer 19

It seems like enough people are helping you so I will just quickly add that

Area of a shaded region = Area of the entire (outer) region - Area of each unshaded region.

Answer 20

Area of side square= side ^2 , therefore, statement 5 is incorrect ..

Answer 21

Can you tell me what should be the area of the white squares in B?

Answer 22

@lilia222
I have to go now. As I said earlier, if you find the sum of the two white squares not equal to 2(x^2+y^2), then your answer would be #5 (i.e. first incorrect answer).

Answer 23

So it is statement 5?

Answer 24

Yes, it is, because it is the first invalid statement, as requested in the question.
Well done! :)