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(C) Let $a$ be the side of the equilateral triangle and $A$ be its area.The area of an equilateral triangle is given by $A = \frac{\sqrt{3}}{4} a^2$.D

Vedclass · Accepted Answer

$20 \sqrt{3} 	ext{ cm}^2/	ext{s}$

Vedclass · Answer

(C) Let $a$ be the side of the equilateral triangle and $A$ be its area.The area of an equilateral triangle is given by $A = \frac{\sqrt{3}}{4} a^2$.Differentiating both sides with respect to time $t$,we get:$\frac{dA}{dt} = \frac{\sqrt{3}}{4} 	imes 2a 	imes \frac{da}{dt} = \frac{\sqrt{3}}{2} a \frac{da}{dt}$.Given that $\frac{da}{dt} = 2 	ext{ cm/s}$ and $a = 20 	ext{ cm}$.Substituting these values into the equation:$\frac{dA}{dt} = \frac{\sqrt{3}}{2} 	imes 20 	imes 2 = 20 \sqrt{3} 	ext{ cm}^2/	ext{s}$.Thus,the rate at which the area is increasing is $20 \sqrt{3} 	ext{ cm}^2/	ext{s}$.

The side of an equilateral triangle is increasing at the rate of $2 \text{ cm/s}$. Find the rate at which the area is increasing when the side of the triangle is $20 \text{ cm}$.

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