*Macmillan Science Library: Mathematics*. Copyright © 2001-2006 by Macmillan Reference USA, an imprint of the Gale Group. All rights reserved.

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## Dimensional Relationships

Usually, when mathematicians compare the size of two-dimensional objects, they compare their areas. For example, how many times larger is a larger square than a smaller one? One way to answer this question is to determine the lengths of the sides of the squares, and use this information to find the respective areas.

Use the formula for the area of a square, *A* = *S*^{2}, where *A* represents area and *S* represents the side length of the square. Suppose two squares have side lengths of 2 and 6, respectively. Hence, the respective areas are 4 and 36. Thus the area of the larger square is nine times that of the smaller square. Therefore, a square whose side length is three times that of a second square will have an area nine times as great.

Use the notation *S*_{1} to denote the side of the smaller square and *S*_{2} to denote the...

This section contains 418 words(approx. 2 pages at 300 words per page) |