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Perimeter rate of a triangle with changing sides

Question

Triangle ABCABC changes over time: ACAC lengthens at 33 units per second, while ABAB and BCBC each shorten at 22 units per second. At time t1t_1 the sides ACAC, ABAB, BCBC measure 1212, 1414 and 1616. At what rate (units per second) is the perimeter changing at t1t_1?

Short answer

−1-1. The perimeter is the sum of the sides, so its rate is the sum of their rates, 3−2−2=−13-2-2=-1; the current lengths are irrelevant.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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