   Chapter 1.1, Problem 59E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

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, A=12×base×height .

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 x2 .

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.

(x2)2+h2=x2x24+h2=

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