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  4. 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

Q. 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

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Solution:

$\alpha+\beta=-b / a: \alpha \beta=c / a \&$
$\alpha+\beta=-c / b: \alpha \beta=a / b$
$\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} $
$\Rightarrow b^{3}=c^{3}$

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