The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 5 cm/s. When the length is 13 cm and the width is 10 cm, how fast is the area of the rectangle increasing?

145 cm²/s

Explanation:

Let the length be 'L', width be 'w' and area be 'A' at any time 't'.

Given:

Rate of increase of length is,

Rate of increase of width is,

Area of the rectangle is given as:

Differentiating both sides with respect to time 't', we get;

Now, we need to find the rate of area increase when L = 13 cm and w = 10 cm. So, plug in all the given values and solve for . This gives,

Therefore, the area is increasing a a rate of 145 cm²/s.

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explanation: