A right triangle has legs of 15 inches and 20 inches whose sides are changing. The short leg is decreasing by 5 in/sec and long leg is shrinking at 6 in/sec.

Question

What is the rate of change of the hypotenuse?

Answer 1

h = sqr(b^2 + a^2), b=15, a=20, b'=-5, a'=-6

h' = [(1/2)/sqr(b^2+a^2)](2bb' + 2aa') = sqr(15^2+20^2)(15(-5)+20(-6)

= (-75-120)/sqr625 = (-195)/25 =-- 39/5 = - 7.8 inches per second

hypotenuse is decreasing at the rate of 7.8 inches per second

check the answer by looking at what happens in one second

short leg goes from 15 to 10

longer leg goes from 20 to 14

hypotenuse goes from 25 to 17.2

25-17.2 = 7.8 decrease in one second. That's -7.8 inches per second rate of change for the hypotenuse