Solve the Problem $a$ And $b$ Are the Lengths of the Legs of a Right Triangle

question 26

Multiple Choice

Solve the problem.
-If $a$ and $b$ are the lengths of the legs of a right triangle and $c$ is the length of the hypotenuse, $c ^ { 2 } = a ^ { 2 } + b ^ { 2 }$ . How is $\mathrm { dc } / \mathrm { d }$ t related to $\mathrm { da } / \mathrm { d }$ t and $\mathrm { db } / \mathrm { dt }$ ?

• A) \(\frac { \mathrm { dc } } { \mathrm { dt } } = \mathrm { a } \frac { \mathrm { da } } { \mathrm { dt } } + \mathrm { b } \frac { \mathrm { db } } { \mathrm { dt } }\)
• B) \(\frac { \mathrm { dc } } { \mathrm { dt } } = \mathrm { a } ^ { 2 } \frac { \mathrm { da } } { \mathrm { dt } } + \mathrm { b } ^ { 2 } \frac { \mathrm { db } } { \mathrm { dt } }\)
• C) \(\frac { \mathrm { dc } } { \mathrm { dt } } = \frac { 1 } { \mathrm { c } } \left( \mathrm { a } \frac { \mathrm { da } } { \mathrm { dt } } + \mathrm { b } \frac { \mathrm { db } } { \mathrm { dt } } \right)\)
• D) \(\frac { d c } { d t } = 2 a \frac { d a } { d t } + 2 b \frac { d b } { d t }\)

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