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

Answer 1

let the short leg be x cm
the longer leg be y cm

given: dx/dt = 1 cm/s, dy/dt = -2 cm/s

Area = (1/2)xy
d(Area)/dt = 1/2[x dy/dt + y dx/dt]

at the given instance, x=5,y=12
d(Area)/dt = 1/2[5(-2) + 12(1)]
= 1 cm^2/s