If the length and width of a rectangle vary with time

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

If the length

x(t)

and width

y(t)

of a rectangle vary with time

t

, which of the following gives the correct rate of change of its perimeter

P

with respect to time? (a)

\displaystyle 2\,\frac{dx}{dt}

(b)

\displaystyle 2\sqrt{\left(\frac{dx}{dt}\right)^2+\left(\frac{dy}{dt}\right)^2}

(c)

\displaystyle 2\Bigl(\frac{dx}{dt}+\frac{dy}{dt}\Bigr)

(d)

\displaystyle \frac{dx}{dt}+\frac{dy}{dt}