Find the instantaneous rate of change when the hypotenuse is 10 cm

Question

The problem:

The area of a 45-45-90 triangle increases at a rate of 3cm^2 per second. What is the instantaneous rate of change of the hypotenuse when its length is 10 cm?

How do I approach this problem? I need to find the derivative of the equation for the hypotenuse, right? I don't know how to set this up.

Answer 1

Area = base times height/2 = A = bh/2

b=h = H/sqr2 = hypotenuse divided by sqr2

it's a 45 45 90 triangle, so both sides are equal to the hypotenuse over square root of 2

A = bh/2 = (H/sqr2)(H/sqr2)/2 = (H^2)/4

take the derivative

A'=(2H/4)H'

A' = HH'/2

3=10H'/2

H' = 6/10 = 0.6 cm/sec