## 1.1: Scaled or Not?

- Which of the geometric objects are scaled versions of each other?
- Pick two of the objects that are scaled copies and find the scale factor.

Let’s explore the U.S. flag.

- Which of the geometric objects are scaled versions of each other?
- Pick two of the objects that are scaled copies and find the scale factor.

One standard size for the United States flag is 19 feet by 10 feet. On a flag of this size, the union (the blue rectangle in the top-left corner) is $7\frac58$ feet by $5\frac38$ feet.

There are many places that display flags of different sizes.

- Many classrooms display a U.S. flag.
- Flags are often displayed on stamps.
- There was a flag on the space shuttle.
- Astronauts on the Apollo missions had a flag on a shoulder patch.

US flag clip art
Copyright Owner:
License:
Public Domain
Via:
openclipart.org

- Choose one of the four options and decide on a size that would be appropriate for this flag. Find the size of the union.
- Share your answer with another group that used a different option. What do your dimensions have in common?

On a U.S. flag that is 19 feet by 10 feet, the union is $7\frac58$ feet by $5\frac38$ feet. For each question, first estimate the answer and then compute the actual percentage.

- What percentage of the flag is taken up by the union?
- What percentage of the flag is red? Be prepared to share your reasoning.

The largest U.S. flag in the world is 225 feet by 505 feet.

- Is the ratio of the length to the width equivalent to $1:1.9$, the ratio for official government flags?
- If a square yard of the flag weighs about 3.8 ounces, how much does the entire flag weigh in pounds?

Imagine you have a painting that is 15 feet wide and 5 feet high. To sketch a scaled copy of the painting, the ratio of the width and height of a scaled copy must be equivalent to $15:5$. What is the height of a scaled copy that is 2 feet across?

width | height | |
---|---|---|

row 1 | 15 | 5 |

row 2 | 2 | $h$ |

We know that the height is $\frac13$ the width, so $h=\frac13 \boldcdot 2$ or $\frac23$.

Sometimes ratios include fractions and decimals. We will be working with these kinds of ratios in the next few lessons.