Answer
$\frac{db}{dt} = -1.6 cm/min$
Work Step by Step
$A = \frac{1}{2} bh$
$100 = \frac{1}{2} b(10)$
$100 = 5b$
$b = 20cm$
$A = \frac{1}{2} bh$
$\frac{dA}{dt} = \frac{1}{2}(h \times \frac{db}{dt} + b \times \frac{dh}{dt})$
$2 = \frac{1}{2}(10 \times \frac{db}{dt} + 20(1))$
$2 = \frac{1}{2}(10 \times \frac{db}{dt} + 20)$
$2 = 5\times\frac{db}{dt} + 10$
$2-10 = 5\times\frac{db}{dt}$
$8 = 5\times\frac{db}{dt}$
Solve for $\frac{db}{dt}$:
$\frac{8}{5} = \frac{db}{dt}$
$\frac{db}{dt} = -1.6 cm/min$
