Folding paper activity question

Question

You are asked to fold an 8.5 x 11 sheet of paper taking one corner of the paper to the midpoint of the non-adjacent 11 inch edge of the paper and make a crease. Without using any measuring device find the length of the crease. I found that the long leg of my triangle is 11-y and the short leg is 102.5/17. I don't know how to find the hypotenuse (length of the crease).

Can we somehow use right triangles again? Similar triangles?

Answer 1

The same way you find the short leg, you can find the long leg.

Draw a right triangle next to the long leg.

The short leg of that new triangle can be expressed as 5.5-(11-y), the hypotenuse is y, and the long leg is 8.5:

(5.5-11+y)² + (8.5)² = y²

Y = 102.5/11

"Y" is the hypotenuse of that triangle and the long leg of your triangle with the crease.