Question

A hypothetical square shrinks at a rate of 49 squared meters per minute. At what rate are the sides of the square changing when the sides are 13m each?

Answer 1

Answer:

-3.769 m/min

Explanation:

$\dfrac{dA}{dt}$ = Rate of change of area = -49 m²/min (negative due to shrinking)

s = Side length = 13 m

$\dfrac{ds}{dt}$ = Rate of change of side

Area of a square is given by

$A=s^2$

Differentiating with respect to time

$\dfrac{dA}{dt}=\dfrac{ds^2}{dt}\\\Rightarrow \dfrac{dA}{dt}=2s\dfrac{ds}{dt}\\\Rightarrow \dfrac{ds}{dt}=\dfrac{dA}{dt}\times \dfrac{1}{2s}\\\Rightarrow \dfrac{ds}{dt}=-49\times \dfrac{1}{13}\\\Rightarrow \dfrac{ds}{dt}=-3.769\ m/min$

The rate of change of the sides of the square is -3.769 m/min