Determine the rate of change of the area of an equilateral triangle with respect to the length of a side.

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Lesson Parent: 
Differentiation V: Derivatives and Rates of Change
Problem: 

Determine the rate of change of the area of an equilateral triangle with respect to the length of a side.

Answer: 

$\frac{\sqrt{3}}{2}s$

SAMPLE SOLUTION

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Solution: 

Recall that the area of an equilateral triangle has the formula

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From this lesson we know that the rate of change of the area with respect to the length of a side is $A'(s)$. Now we know that $A(s)$ is a polynomial function and that the derivative of a polynomial is known. Therefore,

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Suppose that we have an equilateral triangle with the length of its sides being <Sign in to see all the formulas>. The area is

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At a length of <Sign in to see all the formulas>, $A'(s)$ is

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This is best said that at <Sign in to see all the formulas> the area of an equilateral triangle will increase <Sign in to see all the formulas> per <Sign in to see all the formulas> increase in it sides when the length of the triangle's side is <Sign in to see all the formulas>.