In a right triangle, the hypotenuse is of fixed length of 15 units, one side is increasing in length by 4 units per second while the third side is decreasing in size. At a certain instant the increasing side is of length 9 units. Find the rate of change of the third side at the same instant.

Question

In a right triangle, the hypotenuse is of fixed length of 15 units, one side is increasing in length by 4 units per second while the third side is decreasing in size. At a certain instant the increasing side is of length 9 units. Find the rate of change of the third side at the same instant.
Multiple choice answers
a. -3 units per second
b. -5/2 units per second
c. -3/2 units per second
d. -5/4 units per second
e. -3/4 units per second
which on is it? I got -51/8 units per second but that's not right

Steve · Answer

we have x^2+y^2 = 15^2 x dx/dt + y dy/dt = 0 Let x be decreasing, and y increasing. Then when y=9, x=12, and we have 12 dx/dt + 9*4 = 0 dx/dt = -3