<PRE><B>Question 1002659</B>
This is a Pythagorean right triangle problem
a^2 + b^2 = c^2
Let the length of the ladder be x.
One side is x - 16.
The other side is x - 2.
Thus
(x-16)^2 + (x-2)^2 = x^2
x^2-32x+256+x^2-4x+4 = x^2
2x^2 - 36x + 260 = x^2
x^2 - 36x + 260 = 0
(x-26)(x-10) = 0
x = 26 or x = 10
But x cannot be ten since one leg is 16 less.
So the length of the ladder is 26 feet and the distance up the wall is
24 feet.</PRE>