Answer
a) -10 $m^{2}/s$
b) $-\sqrt 2$ m/s
Work Step by Step
Let x be the length of a side and A be the area.
Then A=$x^{2}$, where x is a function of time t.
Now, $\frac{dA}{dt}=\frac{dA}{dx}.\frac{dx}{dt}$ (By chain rule)
Given that $\frac{dx}{dt}$= -1 m/s
Therefore, $\frac{dA}{dt}= 2x(-1 m/s)$
a) When the sides are 5m long,
$\frac{dA}{dy}$=$(2\times5m)$ (-1 m/s)= $-10 \frac{m^{2}}{s}$
b) Let l be the length of the diagonal.
Then l= $x\sqrt 2$
$\frac{dl}{dt}=\frac{d}{dt}(x\sqrt 2 )=\frac{d}{dx}(x\sqrt 2).\frac{dx}{dt}$ (By chain rule)
= $\sqrt 2 \times -1 m/s$= $-\sqrt 2 m/s$
