Problem:
The altitude of a triangle is increasing at a rate of 1cm/min while the area of the triangle is increasing at a rate of 2cm^2/min. At what rate is the base of the triangle changing when the altitude is 10cm and the area is 100cm^2?

Answer: d(base)dt = -1.6.... This is the correct answer from the back of the book.

Im not understanding what is going on in the problem....

Questions:
1. When they say that the altitude is 10cm are they are not saying it is constant are they? It just means at this instant in time it is 10cm... is this correct?

2.Why is the base decreasing? would this mean that the rate of altitude is increasing at such a rate that the base is actually shrinking to compensate for the rate of change in area?

Questions:
1. When they say that the altitude is 10cm are they are not saying it is constant are they? It just means at this instant in time it is 10cm... is this correct?

You are right, they mean that "instant".

2.Why is the base decreasing? would this mean that the rate of altitude is increasing at such a rate that the base is actually shrinking to compensate for the rate of change in area?

Did they specify a type of triangle, or did this problem have a figure?

Most likely though yes, the base was decreasing slow enough that the increase in height allowed for area to be increasing.