Aladder is leaning against a building. the distance from the bottom of the ladder to the building is 8 ft less than the length of the ladder. how high up the side of the building is the top of the ladder if that distance is 11 ft less than the length of the ladder?

assume problem is right triangle with sides (l-8), (l-4), and hypotenuse of l 
pythagorous theorem states c^2 = a^2 + b^2 
l^2 = (l-8)^2 + (l-4)^2 
l^2 = ( l^2 -16 * l +64) + (l^2 -8*l +16) L^2 = 2*l^2 - 24*l + 80 
0 = l^2 -24*l + 80 
factoring 0 = ( l -20) ( L-4) 
l-20 = 0. l=+20 
l-4 = 0, l=4 but l-8 and l-4 are positive lengths therefore l cannot equal 4 
sides of triangle are 20, l-8 = 12, and l-4 =16 ( height up bldg)

L^2 = 2*l^2 - 24*l + 80 
0 = l^2 -24*l + 80 
factoring 0 = ( l -20) ( L-4) 
l-20 = 0. l=+20 
l-4 = 0, l=4 but l-8 and l-4 are positive lengths therefore l cannot equal 4 
sides of triangle are 20, l-8 = 12, and l-4 =16 ( height up bldg)

Your answer is going to be 16.