Step 1
Given the sides the equilateral triangle = $a$ cm
Area of the equilateral triangle is
$ A = \large\frac{\sqrt 3}{4}a^2$
differentiating w.r.t $t$ we get,
$ \large\frac{dA}{d}=\large\frac{\sqrt 3}{4}2a\large\frac{da}{dt}$
But it is given by $ \large\frac{da}{dt}=2 $ cm/sec
when $ a = 10$ cm
$ \therefore \large\frac{dA}{dt_{(a=10)}}=\large\frac{\sqrt 3}{4} \times 2 \times 10 \times 2$
$ = 10\sqrt 3\: cm^2/sec$
Hence option C is the correct answer.