### Home > CALC3RD > Chapter Ch7 > Lesson 7.1.3 > Problem 7-32

A right triangle has a fixed hypotenuse of length

Sketch the triangle and label the known information.

The question is asking about the rate-of-change of area.

So start with an area equation:

Notice that there are two variables. It would be easier to have only one.

Use the Pythagorean Theorem to find the length of the height in terms of .

Then rewrite the function with only one variable:

Implicitly differentiate with respect to time to find a function for

the rate that the area is changing.

Substitute in all values that you know, including the specific base length,

If you did it right, the only variable that will remain is