Question

A rectangle's base remains 0.5 cm while its height changes at a rate of 1.5 cm/min. At what rate is the area changing, in cm when the height is 1.5 cm?

Answer 1

The area of the rectangle is changing at `0.75` **sq.cm/min.**

Explanation:

Let `x and y` be the base and height of the rectangle.

`x=0.5` cm is constant :. dx/dt=0#. Area of the rectangle

is `A=x*y` . Differentiating both sides we get

`(dA)/dt= dx/dt*y +dy/dt*x ;y=1.5, dy/dt=1.5` cm /min.

`:.(dA)/dt= 0*1.5 +1.5*0.5= 0.75` sq.cm/min.

The area of the rectangle is changing at `0.75` sq.cm/min.[Ans]