Question

The sides of an equilateral triangle are increasing at the rate of 4 cm/ sec. the rate at which its area is increasing when the side is 14 cm​

Answer 1

The rate at which its area is increasing when the side is 14 cm​ is 28√3 cm²/s.

• In an equilateral triangle, the length of the three sides of the triangle is equal.

Here, according to the given information, we are given that,

The sides of an equilateral triangle are increasing at the rate of 4 cm/ sec.

Also, we are given that, the length of a side is equal to 14 cm.

Now, area of the equilateral triangle is equal to,

$\frac{\sqrt{3} }{4} x^{2}$ where a is the side of the triangle.

Now, let x be the side. Then, we have that, $\frac{dx}{dt} = 4$.

Now, let X = $\frac{\sqrt{3} }{4} x^{2}$.

Then, $\frac{dX}{dt} = \frac{\sqrt{3} }{4} .2x.\frac{dx}{dt}$

Or, putting the values, we get,

$\frac{dX}{dt} =\frac{\sqrt{3} }{4} .2.14.4\\ = 28\sqrt{3}$

Hence, the rate at which its area is increasing when the side is 14 cm​ is 28√3 cm²/s.

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