### Home > CALC > Chapter 7 > Lesson 7.1.3 > Problem7-33

7-33.

A right triangle has a fixed hypotenuse of length $13$ units. If a leg is increasing in length at a rate of $\frac { 1 } { 2 }$ unit per second, find the rate of change in area of the triangle when that same leg is $5$ units long.

Sketch the triangle and label the known information.

So start with an area equation: $A=\frac{1}{2}bh.$
Use the Pythagorean Theorem to find the length of the height in terms of $b$.
$A=\frac{1}{2}(b)(\sqrt{13^{2}-b^{2}})$
Substitute in all values that you know, including the specific base length, $5$.