Covering Paper using Index Cards

Date: 10/24/2001 at 12:49:21
From: Liz
Subject: This is a question about area.

What is the maximum area of an 8"x13" sheet of paper that you can 
cover by using seven 3"x5" standard index cards?  You may not tear, 
bend, fold, or otherwise mutilate either the paper or the index 
cards, but you may overlap the cards. Explain your thinking.  

I have tried using manipulatives such as an 8x13 sheet of paper and 
the note cards. I have also tried solving this equation mathmatically.  
I know that the area of the seven 3"x5" note cards is greater than 
that of the 8"x13" sheet of paper by one inch; however, when trying to 
cover the 8"x13" sheet of paper I am unable to completely cover the 
whole area of the paper with the notecards. I can cover the whole 
paper if I am able to cut and snip the notecards and paste them over 
the areas, but the directions to not permit this. Is there some other 
way to do it?

I appreciate your help. 
Liz

Date: 10/25/2001 at 09:14:04
From: Doctor Sarah
Subject: Re: This is a question about area.

Hi Liz - thanks for writing to Dr. Math.

You can't cover the whole sheet of 8" x 13" paper, but you can get 
pretty close.  This is what I came up with - see if it agrees with 
your solution:

   

- Doctor Sarah, The Math Forum
  http://mathforum.org/dr.math/   

Date: 10/25/2001 at 21:17:35
From: Elizabeth Delgado
Subject: Re: This is a question in regards to area.

You were right on. Thank you very very much. I have all kinds of brain 
teasers I can now ask you guys about. I appreciate your visual answer; 
you were of great help to me and I will recommend you to everyone I 
know.