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Please solve RD Sharma class 12 chapter 12 Derivative as a Rate Measurer exercise multiple choise question 17 maths textbook solution

Answers (1)

Answer:

8\sqrt{3}\: cm^{2}/hr

Hint:

The area of an equilateral triangle with side a, is defined as,

A(a)=\frac{\sqrt{3}}{4} a^{2}

Given:

\frac{d a}{d t}=8 \mathrm{~cm} / \mathrm{hr} \\ \\ a=2 \mathrm{~cm} \\ W\! e\; have\; to\; calculate\; \frac{d A}{d t}

Solution:

→ Differentiating (i) with respect to t, we get

\begin{aligned} &\frac{d A}{d t}=\frac{\sqrt{3}}{2} a \frac{d a}{d t}\\ \end{aligned}

→ Substituting values, we get

\begin{aligned} &\frac{d A}{d t}=\frac{\sqrt{3}}{2} \times 2 \times 8=8 \sqrt{3} \mathrm{~cm}^{2} / h r \end{aligned}

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