The median of an equilateral triangle is increasing at the rate of 2 V3 cm/s. Find the rate at which its side is increasing.

Let’s denote the side of the equilateral triangle by s, and the median by m.

Since the triangle is equilateral, the median is also equal to the altitude, and it is known that the altitude of an equilateral triangle is equal to (s*sqrt(3))/2.

We want to find ds/dt, the rate at which the side is increasing.

We can use the chain rule to relate the rates of change of s and m:

dm/dt = dm/ds * ds/dt

We know that dm/dt = 2sqrt(3) cm/s, since the median is increasing at a rate of 2sqrt(3) cm/s.

To find dm/ds, we can differentiate the formula for the altitude with respect to s:

m = (s*sqrt(3))/2 dm/ds = (sqrt(3))/2

Now we can substitute the known values into the chain rule equation to find ds/dt:

2*sqrt(3) = (sqrt(3))/2 * ds/dt

Solving for ds/dt, we get:

ds/dt = 4 cm/s

Therefore, the rate at which the side of the equilateral triangle is increasing is 4 cm/s.