Question 408753
Since {{{a}}} is increasing at a constant rate, we can say that the rate of change of a is

{{{da/dt = 3cm/s}}}


Since {{{a^2 + b^2 = c^2 = 169}}} we can write {{{b}}} in terms of {{{a}}}:


{{{b = sqrt(169 - a^2)}}}. Suppose we take the derivative of both sides (we can do this because we have equality for all a,b and their derivatives must be equal). Then,


{{{db/dt = (1/2)(169 - a^2)^(-1/2)(-2a)(da/dt) = -a(169 - a^2)^(-1/2)(da/dt)}}}


When {{{a = 5}}},


{{{db/dt = (-5)(144)^(-1/2)(3cm/s)}}}


{{{db/dt = -5/4}}} (cm/s)