Question

The area of an expanding rectangle is increasing at the rate of 48 cm^2/sec. The length of the rectangle is always equal to the of the breadth. At what rate length is increasing at the instant when the breadth is 4.5cm??

Answer 1

Let the area at time t be A=A (t), and let the breadth at time t be x=x(t). Then the length at time t is x^2, and therefore

A=x^3.

Differentiate with respect to t, using the Chain Rule. We get

dA/dt = 3x^2dx/dt…………………………………………………………(1)

Now freeze the situation at the instant that x=4.5.

We know dA/dt, and we know x, so from (1) we can find dx/dt at that time.