Rate of change of a triangle's perimeter

EasyCalculus~2m

A triangle $ABC$ changes over time: side $AC$ grows at $3$ units/s, side $AB$ shrinks at $2$ units/s, and side $BC$ shrinks at $2$ units/s. At one instant the sides are $12$ , $14$ , and $16$ . At what rate is the perimeter changing (units per second)?

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Perimeter $=$ sum of sides, so $\tfrac{dP}{dt}=$ sum of the side rates.
$3+(-2)+(-2)=-1$ ; the lengths are a distractor.

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Rate of change of a triangle's perimeter

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