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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:

Problem:

Answer:

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

Solution:

Recall that the area of an equilateral triangle has the formula

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,

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

$A'(s)$ is

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>.