Answer
$-1.6$ $cm/min$
Work Step by Step
$A$ = $\frac{1}{2}bh$ where $b$ is the base and $h$ is the altitude
We are given that
$\frac{dh}{dt}$ = $1$ $cm/min$
$\frac{dA}{dt}$ = $2$ $cm^{2}/min$
Product rule
$\frac{dA}{dt}$ = $\frac{1}{2}(b\frac{dh}{dt}+h\frac{db}{dt})$
$h$ = $10$ and $A$ = $100$
$100$ = $\frac{1}{2}(b)(10)$
$b$ = $20$
so
$2$ = $\frac{1}{2}[20(1)+10\frac{db}{dt}]$
$\frac{db}{dt}$ = $-1.6$ $cm/min$
