Question

Jeremy loves right triangles that have side length 1. In fact, he loves to combine them so that the hypotenuse of one becomes the leg of the next. He does this over and over to create beautiful pictures like this:

ASY FAILED

If the longer leg of the first triangle is the square root of 11, what will be the hypotenuse of the 2014th triangle?

Answer 1

I know what diagram you are talking about, it forms a spiral of square roots for the hypotenuse.

hypotenuse of first triangle = √2
hypotenuse of 2nd triangle = √3
hypotenuse of 3rd triangle =√4
...
hypotenuse of nth triangle = √(n-1)

so hypotenuse of 2014th triangle = √2013

Answer 2

Got it

thanks everyone