The rate of change of area is _______ square meters per day.

Question

The base of a right triangle is increasing at a rate of 4 meters per day and the height is increasing at a rate of 1 meter per day.

When the base is 10 meters and the height is 16 meters, then how fast is the area changing?

The rate of change of area is _______ square meters per day.

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

Answer 1

Hello,

For this question, we will need to move forward with the equation of the area of a right triangle:

A = (1/2)*b*h

You will need to take the derivative of this in respect to 't - time', but the only two functions that are define to have 't-time' are the ones that are changing from the premise of the question. (rate of change of base = 4m, rate of change of height = 1m)

So that means from the above equation...

b = b(t) and h = h(t).

This means that you will move forward with taking the derivative of 'A' in respect to 't-time' and notice that (b*h) is a product of one another and you're trying to draw out (db/dt) and (dh/dt) (A calculus 'rule' is defined to draw those). The rest is just plugging in what we know from the premise and viola!

I hope this helps!