The base of a right triangle is decreasing at a rate of 3 meters per day and the height is decreasing at a rate of 5 meters per day.

Question

When the base is 9 meters and the height is 17 meters, then how fast is the AREA changing?

The rate of change of AREA is _____ square meters per day.

(Enter your answer as an integer or as a decimal number rounded to 2 places.)

Answer 1

The base decreasing 3 meters per day means:

db/dt = -3

The height decreasing 5 meters per day means:

dh/dt = -5

The formula for the area of a triangle is:

A = 1/2 * b * h

Use implicit differentiation and the product rule to find dA/dt:

dA/dt = 1/2 * b * dh/dt + 1/2 * db/dt * h

Plug in the values that we have for base, height, change in base, and change in height:

dA/dt = 1/2 * 9 * (-5) + 1/2 * (-3) * 17

dA/dt = -48

So the rate of change of the area is -48 square meters per day.