Question

The area of an isosceles right triangle decreases at a rate of 5 cm² per second. At what rate is the hypotenuse changing when each of the other sides has length 10 cm?

So far I have:
Given: dA/dt= 5cm^2/s
Find: dH/dt when b&h= 10cm

And h= root 200(?)

Answer 1

let each of the equal sides be x cm
A = (1/2)x^2
dA/dt = x dx/dt
we know dA/dx = -5 cm^2 /s
dx/dt = -5/x

H^2 = x^2 + x^2 = 2x^2
H = √2 x

dH/dt = √2 dx/dt = √2(-5/x)
so when x = 10
dH/dt = -5√2 /10 = -(1/2)√2 cm/s
or appr -.707 cm/s