(details below) legs of a right triangle - If one leg increases, other decreases how fast does area change?

Question

At a given instant, the legs of a right triangle are 5 cm and 12 cm long. If the short leg is increasing at the rate of 1 cm/sec and the long leg is decreasing at the rate of 2 cm/sec, how fast is the area of the triangle changing?

Answer 1

2A = x*y 2dA = ydx+xdy
now dividing by dt
2dA/dt = ydx/dt +xdy/dt = 5*2+12*1 = 22
so dA/dt = 11cm^2/s