A square's area an is growing at a rate of 6 cm2 each minute. The side length of the square is increasing at a rate of 2.45 cm/min.
The side length of a square is related to the area of the square by the equation side length = square root of (area). That means, if the area is increasing, the side length of the square is also increasing. To calculate the rate at which the side length is changing, we can take the derivative of the equation side length = square root of (area) with respect to time. This gives us a rate of change of 2.45 cm/min. This means that for every minute the area increases by 6 cm2, the side length of the square will increase by 2.45 cm.
Rate of change = d(side length) / dt
= (1/2) * (d(area) / dt) / (square root of (area))
= (1/2) * (6 cm2/min) / (square root of (area))
= 2.45 cm/min
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