Question

The rate of variable reactangle is increasing at rate of 60 cm square / second . The length of the reactangle is always equal to the square of the breadth.At what rate the length is increasing at the instant where the breadth is 4cm?

Answer 1

Let the breadth (width ?) be x
then the length = x^2

area = width*length = x(x^2) = x^3
d(area)/dt = 3x^2 dx/dt

given: d(area)/dt = 60
find d(length)/dt when x = 4

60 = 3(16) dx/dt
dx/dt = 5/4

length = x^2
d(length)/dt = 2x dx/dt, so when x = 4
d(length)/dt = 2(4)(5/4) = 10

I skipped the units for convenience's sake, so

d(length)/dt = 10 cm/s