Question

An equilateral triangle made of metallic sheet is expanding because it is being heated. Its area A is given by

A =(√3x^2)/4

square centimeters, where x is the length of one side in centimeters. Find the instantaneous rate of change in A with respect to x at the instant when x = 10 centimeters.

Answer 1

$$A_x=\dfrac{\sqrt{3}}{4}(2x)=\dfrac{\sqrt{3}x}{2}$$

$x=10\ cm$

$$A_x=\dfrac{\sqrt{3}(10)}{2}=5\sqrt{3}(cm^2/cm)$$

The instantaneous rate of change in A with respect to x at the instant when x = 10 centimeters is

$5\sqrt{3}\ cm^2/cm$