The length and width of a rectangle are increasing at constant rates of and

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

The length

x

and width

y

of a rectangle are increasing at constant rates of

5\text{ cm/min}

and

2\text{ cm/min}

, respectively. When

x=12\text{ cm}

and

y=5\text{ cm}

, what is the rate at which the length of the rectangle’s diagonal is increasing? (a)

\dfrac{50}{13}\text{ cm/min}

(b)

\sqrt{29}\text{ cm/min}

(c)

\dfrac{70}{13}\text{ cm/min}

(d)

\dfrac{85}{13}\text{ cm/min}