SOLUTION: The base of a right triangle is decreasing at a rate of 2 inches per minute, and the height of the triangle is increasing at a rate of 4 inches per minute. When the base of the tri

Question 855600: The base of a right triangle is decreasing at a rate of 2 inches per minute, and the height of the triangle is increasing at a rate of 4 inches per minute. When the base of the triangle is 2 feet and the height is 3 feet, how fast is the area of the triangle changing in square inches per minute?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The way I see it, this is a calculus problem.
With = time (in minutes) counted from the moment the base of the triangle is 2 feet and the height is 3 feet,
the base (in inches), height (in inches), and area (in square inches) are all functions of :

The rate of change of the area (in square inches per minute) is
which changes with time.
At (the moment the base of the triangle is 2 feet and the height is 3 feet)

Without invoking calculus, the only solution I see is saying that the rate is the slope of the tangent to the graph.
With and the graph would be
.
The tangent , with slope passes through the origin
and intersects at only one point.
That means that must have only one solution.
<--><--><-->
has the solutions and .
Those solutions are the same only when <--> ,
which makes the line tangent.
A line with another slope would intersect the graph at two different points, with , and .
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