BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 4, Problem 18P
To determine

The maximum and minimum areas that the triangle AEF can have.

Expert Solution

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.

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 4, Problem 18P

Now E can be anywhere on AB and F can be anywhere on AD. Now Area of the triangle AEF is,

  Area of ΔAEF=12AE×AF.   Since ΔABD is a right angle triangle and A=90°. 

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,

  Area of ΔAEF=12AE×AF.   Taking AE=AB and AD=AFArea of ΔAEF=12AD×AE= 12×1×1=0.5m2

Now the minimum area of the triangle is,

  Area of ΔAEF=12AE×AF.   Taking E very close to A and D very close to A.Area of ΔAEF=12AD×AE0m2

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