Related Rates Calculus

Question

A ladder is sliding down a wall. At the instant when the top of the ladder is 12m from the ground, the base of the ladder is sliding away form the wall at 6m/s and the top of the ladder is descending at 8m/s. How long is the ladder?

Answer 1

dy/dt = -8 and dx/dt = 6, so dy/dx = -8/6 = -4/3

y = sqrt(L^2 - x^2); dy/dx = -x/sqrt(L^2 - x^2) = -x/y

-x/12 = -4/3; -3x = -48; x = 16

L = sqrt(16^2 + 12^2) = 20