Answer:
The base of the triangle is decreasing at a rate of 1.4167 inch/hour.
Step-by-step explanation:
Area of a triangle:
The area of a triangle of base b and height h is given by:
In this question:
We have to derivate the equation of the area implicitly in function of time. So
The altitude of a triangle is increasing at a rate 2 inch/hour while the area of the triangle is decreasing at a rate of 0.5 square inch per hour.
This means that:
At what rate is the base of the triangle is changing when the altitude is 6 inch and the area is 24 square inch?
This is when
Area is 24, so the base is:
Then
The base of the triangle is decreasing at a rate of 1.4167 inch/hour.