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?

Feb 8, 2018

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

Explanation:

Let $x \mathmr{and} y$ be the base and height of the rectangle.

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

is $A = x \cdot y$ . Differentiating both sides we get

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

$\therefore \frac{\mathrm{dA}}{\mathrm{dt}} = 0 \cdot 1.5 + 1.5 \cdot 0.5 = 0.75$ sq.cm/min.

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