Question

At an instant the diagonal of a square is increasing at the rate of $0.2cm/sec$ and the area is increasing at the rate of $6{cm}^2/sec.$ At the moment its side is

• A. $\frac{30}{\sqrt{2}}cm$
• B. $30\sqrt{2}cm$
• C. $30cm$
• D. $15cm$

Answer 1

Answer: (A)

$\frac{30}{\sqrt{2}}cm$

Length of diagonal of square $l=x\sqrt{2}$

$\Rightarrow \frac{dl}{dt}=\sqrt{2}\frac{dx}{dt}$

$\Rightarrow \frac{dx}{dt}=\frac{0.2}{\sqrt{2}}$ cm/sec

Area of square $A=x^2$

$\frac{dA}{dt}=2x\frac{dx}{dt}$

$\Rightarrow x=\frac{30}{\sqrt{2}}$ cm