If I had a 20' piece of rope and at the center (10') raised it 6'. How do I fiqure out the distance between the two ends?

Question

 

 

                                                                                    _

                                                                                     l

                                                                                    6'   

                                   _____ 20'_____                _         l        _

                                                                                     ?

Answer 1

By raising the rope 6 feet, this creates 2 triangles (right) with height of 6 feet, and each side of rope then being a hypotenuse of each triangle of 10 feet. Square of hypotenuse is equal to squares of other two legs, of which we have one, 6 feet. So, 10 feet squared (hypotenuse), is 100, other leg squared, 6 feet squared is 36, 100 minus 36 is 64, of which the square root is 8, so each triangle has length of 8 feet, so from rope end to rope end is 2 times 8, or 16 feet.