Each side of a square is increasing at a rate of 5 cm/s. At what rate is the area of the square increasing when the area of the square is 36 cm2

The area of the square is increasing at a rate of 60 cm²/s

Step-by-step explanation:

Let be the length of the side of the square

Hence, The area of the square is given by

Where is the area of the square

From the question, each side of a square is increasing at a rate of 5 cm/s, that is,

Now, to determine the rate at which the area of the square is increasing, That is

To find , differentiate with respect to

From,

×

×

Now, to determine the rate at which the area of the square is increasing when the area of the square is 36 cm²

First, we will determine the length at this instance,

From,

The length at this instance is 6cm

To determine the rate at which the area of the square is increasing at this instance

From the question,  

Hence,

×

×

Hence. the area of the square is increasing at a rate of 60 cm²/s

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