Answer: the area is increasing at 138 cm²/s
Step-by-step explanation:
Let L represent the length of the rectangle.
Let W represent the width of the rectangle
The formula for the area of the rectangle is expressed as
Area = LW
Since the length and width is increasing, we would apply the product rule to determine the rate at which the area is also increasing.
dy/dx = udv/dx + vdu/dx
L = u, W = v and x = t because it is changing with respect to time. Therefore,
dA/dt = Ldw/dt + Wdl/dt
From the information given,
L = 15cm
W = 6 cm
dw/dt = 8cm/s
dl/dt = 3cm/s
Therefore,
dA/dt = (15 × 8) + (6 × 3)
dA/dt = 120 + 18
dA/dt = 138 cm²/s
Given :
The length of a rectangle is increasing at a rate of 3cm/s and its width is increasing at a rate of 8 cm/s.
When the length is 15 cm and the width is 6 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 = 15*8 + 6*3
dA/dt = 120 + 18 cm²/s
dA/dt = 138 cm²/s
