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provide solution for rd sharma maths class 12 chapter 12 derivatives as a rate measure exercise  fill in the blanks question 6

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Answer: 10\sqrt{3}cm^{2}/s

Hint: Let the side of cm equilateral triangle be x\; cm

Given: \frac{dx}{dt}=2cm^{2}/s

            Area of equilateral triangle A=\frac{\sqrt{3}}{4}x^{2}                  .......(i)                                                             

Solution: Differentiating equation \left ( i \right )  with respect to x we get

                   \frac{dA}{dt}=\frac{\sqrt{3}}{4}\times 2x\times \frac{dx}{dt}

                        = \frac{\sqrt{3}x}{2}\frac{dx}{dt}

           When x= 10

                  \frac{dA}{dt}=\frac{10\sqrt{3}}{2}\times 2=10\sqrt{3}\; cm^{2}/s

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