Concept explainers
To find: The function of the area of an equilateral triangle in terms of the length of the side and the function domain.
Answer to Problem 55E
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
Explanation of Solution
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
Chapter 1 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning