Pythagorean's Perfect Square, a²+b²=c² Mystery Cache

Pythagoras' theorem: a²+b²=c²
When you have a triangle with a 90° angle, it becomes possible to find the lenght of the Hypotenuse, by adding the squares of the two sides adjacent to the 90° angle, and then taking the square root of that total.
 

This cache is being released on 2016/04/04, or in other words, Perfect Square Day. Look it up: http://squarerootday.net/

Now why is that so fun? or even bloody necessary?

Well, I'm sure most everyone has climbed a ladder.  but a 12 foot lader, leaned against a house, will not reach 12 feet vertically.  The ladder is the Hypotenuse.

There are many other uses, and I use it almost every day in my survey work, sure, I let a computer do most of the work, but knowing it's function, helps me to dive deep into geometry theory and draw the circles and arcs I need by simply understanding the basic function of a square triangle.

A fellow cacher, Captain Math, released a Pi Day event and puzzle cache a few weeks ago, also on a monday, on Pi day, and when I discovered that there was an actual day for Perfect Square day, and being a lover of Geometry and all the Pythagoreas has done for geometry, I asked him if he was interested in an event for Perfect Square day, so he obbliged and you can read all about it here on his event page.  

There are many other uses for a triangle with a square angle, and shortcuts so you don't need the crazy math. Like a 3-4-5 triangle. If the two sides adjacent to the square angle are 3 and 4, then the Hypotenuse is exactly 5. WOW. Awesome!!!  and the same for multiples of the numbers.  6-8-10, etc...

See attached Image for the the puzzle. 

You can check your answers for this puzzle on GeoChecker.com.