Start your trial now! First week only $4.99!*arrow_forward*

BuyFind*launch*

4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.1, Problem 55E

To determine

**To find:** The function of the area of an equilateral triangle in terms of the length of the side and the function domain.

Expert Solution

The formula for the function of area of an equilateral triangle in terms of the length of side is

The domain of the function of the area (*A*) of an equilateral triangle in terms of length of the side is

**Formula used:**

Area of the equilateral triangle,

**Calculation**:

Let the side length of the equilateral triangle be *x.*

Obtain the height of the equilateral triangle as follows:

Draw a line from any vertex to its opposite side so that it makes two equal right angled triangles.

Consider any one of the right angled triangle.

Since the side of the equilateral triangle is *x*, the base of the right angled triangle is

Let the height of the right angled triangle be *h*. Note that the height of the right angled triangle is the height of the equilateral triangle.

Apply Pythagoras theorem and obtain the value of height.

Therefore, the height of the equilateral triangle is

Thus, the area of the equilateral triangle is

Therefore, the function of the area of an equilateral triangle in terms of its length of a side is

The domain of the function of the area (*A*) of an equilateral triangle in terms of length of side is
*x* cannot take the negative values.