Question

Perimeter of a square increase at the rate of 0.4 cm /sec. when the side is 20cm, its area increase at the rate of

• A. $0.4c{m}^2/sec$
• B. $0.8c{m}^2/sec$
• C. $0.2c{m}^2/sec$
• D. $4c{m}^2/sec$

Answer 1

The correct option is D $4c{m}^2/sec$

Let side of square$=$a cm

$\Rightarrow$ P$=$ perimeter $=4a$

$\Rightarrow \frac{dP}{dt}=\frac{4da}{dt}=0.4$

$\Rightarrow \frac{da}{dt}=0.1$

$A=$ Area $=a^2$

$\Rightarrow \frac{dA}{dt}=\frac{d{a}^2}{dt}=2a\frac{da}{dt}=2\times 20\times 0.1=4c{m}^2/sec$.

$\Rightarrow$ (D).