Question

The sides of an equilateral triangle are increasing at the. rate of $2 \,cm / sec$.The rate at which the area is increases when the side is $10\, cm$.is

• A. $\sqrt{3}$ sq . units / sec
• B. $10$ sq. units/sec
• C. $10 \sqrt{3}$ sq. units / sec
• D. $\frac{10}{\sqrt{3}} $ sq. units/sec

Answer 1

Answer: (C)

$\alpha+\beta=-b / a: \alpha \beta=c / a \&$
$\alpha+\beta=-c / b: \alpha \beta=a / b$
$\therefore-\frac{b}{a}=-\frac{c}{a} \&-\frac{c}{a}=\frac{a}{b} $
$\Rightarrow b^{2}=a c: a^{2}=b c$
$\Rightarrow b^{4}=a^{2} c^{2}=b c \cdot c^{2}=b c^{3} $
$\Rightarrow b^{3}=c^{3}$