A right triangle has legs of 18 inches and 24 inches whose sides are changing. The short leg is decreasing by 7 in/sec and the long leg is growing at 3 in/sec. What is the rate of change of the area?

Answer 1

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The area is decreasing at the rate of 57 in² / sec.

I solved this using Product Rule of Derivatives + Related Rate of change concept.

Answer 2

Let's set the two legs as a and b, so the lengths are:

.

So the area is:

,

and the rate of change of the area is:

.

And at t=0, the rate is -57 in²/s.

Answer 3

A=(1/2)Bh

dA/dt = (1/2)[ B dh/dt + dB/dt H ]

= (1/2) ( 24*3 + 18 * -7)

1/2*(72-126]= -50