A triangular lamina whose base length is twice its corresponding height is expanding while maintaining its shape. Find the average rate of change in its area when its height varies from 14cm to 23cm.
Let the height of the triangle be denoted by and the base length be denoted by . Then the area of the triangle is given by
The average rate of change of the area as the height varies from cm to cm can be found as follows:
Therefore, the average rate of change of the area as the height varies from cm to cm is .