To express: The length of the hypotenuse as a function of the perimeter.
Answer to Problem 2P
Solution:
The length of the hypotenuse is
Explanation of Solution
Given:
The altitude perpendicular to the hypotenuse
Formula used:
Pythagoras theorem
Where, h is a hypotenuse, and x, y is the sides of triangle
Perimeter of the triangle
Calculation:
Consider the triangle as shown below in the Figure 1.
From the Figure 1,
Substitute
From the equation (1),
This implies
Consider the equation
Substitute the values of equation (1) and equation (2) in above equation,
From equation (3),
Substitute the value of
Substitute
On further simplification, the value of
Therefore, the length of the hypotenuse 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