Hi! I'm SO SORRY that this is REALLY late. I hope that I explain this question well. The Question I got is the chessboard question. THe first question talks about the diagonal lines of the small squares/rectangles.

**A)Find the diagonal of all squares and rectanges possible in the first three rows. Then Arrange the squares/rectangles, from least to greatest by length of their diagonals.**

As you can see, not all the little squares were "counted" because for example, row 3 and column 1 was already done by the first row, third column.(Do you get it?)

Now we need to find

**ALL**

**the possible diagonals**in the first three rows.

If it helps you draw a picture of the chess board and then do the math.

The picture(sorry that it's a bit blurry)on the bottom shows all the possible diagonal lines.

**IN ORDER**from**LEAST TO GREATEST**In order to get the diagonal of the squares/rectangle, you need to know that

**A squared + B squared = C squared (formula for a triangle)**The second part of this question is...

**B) Consider the entire chessboard. When would you expect the square or rectangle to give a whole number diagonal?**

The picture below shows how many squares/rectangles that give a whole number. When we did the three rows, we only found one.

**Which was 3 squared + 4 squared = C squared**

**Then the square root of 10 = C squared**

**Then the answer was 5 = C squared**

Then there's another diagonal with a whole number which was:

**6 squared +8 squared = C squared**

**square root of 100 = C squared**

**Then you get the answer of 10 = C squared**

If you look at the two diagonals that have a whole number as a diagonal, you could see that

6 squared +8 squared is four times as much as 3 squared + 4 squared. I don't really know how else I could explain part B of this question....so that's all I'm going to say...