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### 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?

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

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

```
Date: 10/25/2001 at 21:17:35
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
you were of great help to me and I will recommend you to everyone I
know.
```
Associated Topics:
High School Euclidean/Plane Geometry
High School Geometry
High School Triangles and Other Polygons
Middle School Geometry
Middle School Triangles and Other Polygons
Middle School Two-Dimensional Geometry

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