Browse Questions

# If the length of the diagonal of a square is increasing at the rate of $0.1 cm/sec.$ What is the rate of increase of its area when the side is $\large\frac{15}{\sqrt{2}}$cm?

$\begin{array}{1 1}(1)1.5 cm^{2}/sec&(2)\frac{1}{2\pi}\\(3)4\pi&(4)\frac{\pi}{3}\end{array}$

Let a be the length of the side , d the length of the diagonal and A be the area of the square at time t.
$A=a^2$
$d^2=a^2+a^2= 2a^2$
$d= \sqrt 2 a$