Question

The length of each leg of an isosceles right triangle is increase at the rate of 2 mm/s. How fast is the hypotenuse increasing at the moment when each leg is 10 mm?

Answer 1

h^2 = 2 x^2

2 h dh/dx = 4 x

dh/dx = 2 x/h

dh/dt = dh/dx * dx/dt = 2 (x/h) dx/dt
but x/h = 1/sqrt 2
so
dh/dt = sqrt 2 * dx/dt
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but more simply
h = x sqrt 2
dh/dx = sqrt 2