Concept explainers
The maximum and minimum areas that the triangle AEF can have.
Explanation of Solution
Given information:
ABCD is a square piece of paper with sides of length 1m. A quarter circle is drawn from B to D with center A. The piece of paper is folded along the EF, with E on AB and F on AD so that A falls on the quarter circle.
Calculations:
Here according to the given information we draw the diagram.
Now E can be anywhere on AB and F can be anywhere on AD. Now Area of the triangle AEF is,
Now the area of the triangle will be maximum if E is very close to B and F is very close to D.
Also the area of the triangle will be minimum if E is very close to A and F is very close to A.
Therefore maximum area of the triangle is,
Now the minimum area of the triangle is,
Chapter 4 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