Chapter 1.1, Problem 59E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

Find a formula for the described function and state its domain.

**59.** Express the area of an equilateral triangle as a function of the length of a side.

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.

Explanation

**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.

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