*Contributor: Jamie Hagler. Lesson ID: 13841*

Plan on completing this lesson to learn how to create and use scale drawings!

categories

subject

Math

learning style

Visual

personality style

Golden Retriever

Grade Level

High School (9-12)

Lesson Type

Skill Sharpener

- How do you know if your house was burgled by Smurfs?

Look for blueprints!

^{Image [cropped and shoe prints added] by Edouard Jausions, via Pixabay, was released into the public domain.}

All kidding aside, we will be talking about scale drawings, and blueprints are the perfect scale drawing!

First, let's talk about scale.

*Scale* is the ratio between corresponding measurements of a blueprint and the actual object.

In the example below, the blueprint is 1 inch by 3 inches, while the actual object is 4 inches by 12 inches:

In this example, the scale would be 1:4. This means that for every 1 unit on the blueprint, there are 4 units on the actual object.

This could possibly mean that 1 unit (maybe an inch) on the blueprint could represent 4 inches (or even 4 feet!) on the actual object.

Let's do a basic scale problem:

Jim made a blueprint of the White House. Jim's blueprint used a scale in which 1 inch represents 6 feet. The White House has an actual length of 168 feet.

- What is the length in inches of Jim's blueprint?

We can solve this by setting up a proportion!

We will put the inches on the top of each fraction and feet on the bottom. We then cross-multiply and divide:

inches | = | inches | |

feet | feet |

1 | = | x | |

6 | 168 |

168 | = | 6x | |

6 | 6 |

28 | = | x |

Therefore, 28 inches is the length in inches of Jim's blueprint

- Not too bad, huh?

Here's another one:

Lisa Ann drew the following blueprint of her store:

- If 1 inch = 4 feet, what is the area of the store?

This one is a little different and involves one more step, but we've got this!

- First, what would the dimensions of the store be?

We can set up proportions like before. However, this time we need to determine two different answers: the length and width in feet of the store.

inches | = | inches | inches | = | inches | ||

feet | feet | feet | = | feet |

1 | = | 5 | 1 | = | 9 | ||

4 | x | 4 | = | x |

20 | = | x | 36 | = | x |

We can see the dimensions of the store would be 20 feet by 36 feet:

- The question asked for the area of the store, so are we finished?

Nope! One more step!

- How do we find area of a rectangle?

The formula is *A* = *lw*, so we will multiply the length and width. This will give us 20 x 36, which is 720.

Therefore, the area of the store is 720 square feet!

Now that you have a handle on using and describing scale drawings, let's move on to the *Got It? *section.

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