Question 370605
From the information given, the hypotenuse is l, the horizontal leg is l - 16, and the vertical leg is l - 8.  Using the Pythagorean theorem, then {{{l^2 = (l-8)^2+(l-16)^2}}}.
{{{l^2 = l^2-16l+64 + l^2 - 32l+256}}}, or
{{{0 = l^2 - 48l+320}}}, or
0 = (l-40)(l-8).  Thus l = 40 ft or l = 8 ft.  We discard the 2nd value (why?)  Thus the length of the ladder is 40 feet.