Carpet Layer a Geometric Puzzler

[stahrwe]

Many years ago a carpet layer showed this puzzle to me. His question was whether the area a given piece of carpet covered was constant or not. I said, 'Of course'. He proceeded to tell me he could cut a 64 sf piece of carpet and cover 65 sf area. He was right or there would be no reason for this puzzle. The puzzler is, 'how did he do it'?

Hint, start with a piece of paper and draw an 8" by 8" square.

[stahrwe]

Draw a line straight across the paper at 5"
You will now have two rectangles

a 5" by 8"
and

a 3" by 8"

[Interbane]

Do you do something special with those rectangles?

[stahrwe]

Divide the 3" by 8" rectangle into two equal right triangles.

There is one more step after this one and then you will cut apart the figures into four pieces which you will rearrange into a rectangle.

If you can figure out the final line to draw on the 5 by 8 rectangle post the endpoints otherwise I will provide the solution tomorrow.

[stahrwe]

Lay the 5 by 8 rectangle out and draw a diagonal from the 5 inch point to the 3 inch point on the long side.

Cut the rectangle into two pieces along the line.

Now take these pieces and the two right triangles and arrange them into a rectangle with sides 5 by 13

You started with a square 8 by 8 = 64 si
now you have a rectangle 8 by 13 = 65 si

How is that possible?

[johnson1010]

the slopes of your cuts are not the same.
In the difference lies the area of the additional apparent square inch.

[Interbane]

The problem would become obvious if decimal points were included, I assume.

[stahrwe]

the slopes of your cuts are not the same.
In the difference lies the area of the additional apparent square inch.

Why didn't you post the slopes?

3/8
2/5

15/40
16/40


Did you get the point?

[johnson1010]

oh, sorry.

Thought maybe other people could check into it as well.

Yeah, i broke out my highly out of shape math skills.