MathematicsThe side of an equilateral triangle expands at the rate of 2 cms/sec. The rate of increase of its area when each side is 10cms. Is –––––sq cms/sec.

The side of an equilateral triangle expands at the rate of 2 cms/sec. The rate of increase of its area when each side is 10cms. Is –––––sq cms/sec.

Solution:

$\frac{d x}{d t} = 2 c m / \sec, x = 10, A = \frac{\sqrt{3}}{4} x^{2} \frac{d A}{d t} = \frac{\sqrt{3}}{4} (2 x) \frac{d x}{d t} = \frac{\sqrt{3}}{2} (10) 2 = 10 \sqrt{3}$

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