Answer
$140$ cm/s
Work Step by Step
Given information: $\displaystyle \frac{dl}{dt} = 8 $ cm/s, $\displaystyle \frac{dw}{dt} = 3 $ cm/s, $ l = 20 $ cm, $w = 10$ cm
What we're trying to find: Change in area with respect to time ($\displaystyle \frac{dA}{dt}$)
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$A = wl$
We must implicitly differentiate using the product rule:
$\displaystyle \frac{dA}{dt} = w\cdot \frac{dl}{dt} + l\cdot \frac{dw}{dt}$
Now plug in the givens:
$\displaystyle \frac{dA}{dt} = 10(8) + 20(3)$
$\displaystyle \frac{dA}{dt} = 140$ cm/s
