Geometry and Right Triangles

The diagram of above shows the relationship between the area of the large purple square and the area of the middle tan colored square.  The website Math is Fun tells how how this puzzle fits together.  The right triangles and squares inside the figure create a unique pattern that we use today to find out the length of the sides of right triangles.  

Use this Pythagorean Theorem interactive tool to experiment with how the sum of the squares of the triangle legs is equal to the longest side squared.

Here's a Pythagorean Theorem problem to try. Take a moment also to share your own problem as well.
A ladder stretches from the floor to a shelf diagonally. (c)  The distance from the floor to the base of the ladder is 4 meters (b).  The height of the wall which makes a 90 degree angle with the floor is 3 meters (a).  What is the length of the ladder?

3*3  + 4*4=  ___ * ___

9  + 16  = ___ * ___

25 = ___ * ____           Hint: square root of 25 = ?
How many meters long is the ladder?