The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of 8 cm/s. When the length is 8 cm and the width is 5 cm, how fast is the area of the rectangle increasing?

Given :

The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of 8 cm/s. When the length is 8 cm and the width is 5 cm .

To find :-

how fast is the area of the rectangle increasing?

Solution :-

As we know that :-

A = lb

To find the rate :-

d(A)/dt = d(lb)/dt .

Differenciate :-

dA/dt = l (db/dt ) + b (dl/dt )

Substitute :-

dA/dt = 8*8 + 5*4dA/dt = 64 + 20 cm²/s dA/dt = 84 cm²/s

Iwould say they are complementary because that’s the division of a 90 degree angle and it’s split between the middle of them

Ithink it is b and d