Answer to Question #345338 in Calculus for Ben

Question

The base of a rectangle is changing at the rate of 3 in/min. If its height remains constant, determine the rate of change of its perimeter with respect to time.

Answer 1

Let $x=$ the base of a rectangle, $h=$ the height of a rectangle.

$$P=2x+2h$$

Differentiate with respect to $t$

$$dP/dt=2dx/dt+0$$

Given that the base of a rectangle is changing at the rate of 3 in/min.

Then the perimeter of a rectangle is changing at the rate of 6 in/min.