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### Course: 7th grade (Illustrative Mathematics)>Unit 1

Lesson 8: Lesson 11: Scales without units

# Scale drawing word problems

Use scale drawings to solve problems in real-world contexts.

## Practice problem 1: Two figures

Problem 1
Figure $A$ is a scale image of Figure $B$.
What is the value of $x$?

## Practice problem 2: Map

Problem 2
Alexander is drawing a map of the Federal Triangle in Washington, D.C. The actual Federal Triangle has a base of $3000$ feet and height of $1200$ feet. Alexander needs his drawing to fit on his paper, so he decides to make the base of his triangle $10$ inches.
What scale is Alexander using?
:
$\text{feet}$
What is the height of Alexander's triangle in inches?
$\text{inches}$

## Practice problem 3: Scale model

Problem 3
Rena is building a $1:180$ scale model of a real castle. Her model has a rectangular base that is $3$ feet wide and $4$ feet long.
What is the area of the base of the actual castle in square feet?
$\text{square feet}$

## Practice problem 4: Moon challenge

Problem 4
The earth is approximately $8000$ miles in diameter. The moon is approximately $2000$ miles in diameter. The distance between the two is approximately $240,000$ miles.
You build a two-dimensional scale model of the earth and moon. You use a circle with a diameter of $1$ inch to model the moon.
In your model, what is the diameter of the earth in inches?
inches
In your model, what is the distance between the moon and the earth in inches?
inches

## Want to join the conversation?

• who introduced scale drawing
• A really smart demon
• why am i struggling so bad with basic math lol
• I wanna know the same thing lol , I just got mad for no reason this is basic stuff lol
• f whoever made math like wth
• com on your not him
• The first two questions are kinda hard to understand. Can someone simplify them for me?
• for number two its 1 inch for 300 feet its easy for the second part after that
• This was so confusing I did not get it at all
• this is the most confusing thing ever
• fr fr
• I is confused with problem 1,3,4. Plz help
• #1- If diagram A is the scaled image of diagram B, then diagram B is the original. If you were to set up a ratio, it would look something like this:
3 : 4
x : 7.2
Using this, you can figure out x. 7.2 / 4 = 1.8, which you multiply by 3 to get 5.4 (which is the answer).

#3- They tell you the scale is 1 : 180. In this case, it means that 1 ft (in the model) is equal to 180 real ft.
Width: 3 model ft = 3 x 180 = 540 real ft
Length: 4 model ft = 3 x 180 = 720 real ft
Then, to find the area of the real castle, you multiply 540 by 720 to get your answer: 388,800 sq. ft.

#4- The problem tells you that the moon has a diameter of 2,000 miles in real life. In the model, the moon has a diameter of 1 inch. Using this information, you can figure out the scale: 1 model inch = 2,000 real miles. So if the Earth is 8,000 miles in diameter, then the model Earth would be 4 inches in diameter. Finally, if the distance between them is 240,000 real miles, then the model distance between them would be 120 inches.

Sorry if it's a little wordy. Hope this helps!