Lesson 12
Units in Scale Drawings
Let's use different scales to describe the same drawing.
Problem 1
The Empire State Building in New York City is about 1,450 feet high (including the antenna at the top) and 400 feet wide. Andre wants to make a scale drawing of the front view of the Empire State Building on an \(8 \frac{1}{2}\)-inch-by-\(11\)-inch piece of paper. Select a scale that you think is the most appropriate for the scale drawing. Explain your reasoning.
- 1 inch to 1 foot
- 1 inch to 100 feet
- 1 inch to 1 mile
- 1 centimeter to 1 meter
- 1 centimeter to 50 meters
- 1 centimeter to 1 kilometer
Problem 2
Elena finds that the area of a house on a scale drawing is 25 square inches. The actual area of the house is 2,025 square feet. What is the scale of the drawing?
Problem 3
Which of these scales are equivalent to 3 cm to 4 km? Select all that apply. Recall that 1 inch is 2.54 centimeters.
0.75 cm to 1 km
1 cm to 12 km
6 mm to 2 km
0.3 mm to 40 m
1 inch to 7.62 km
Problem 4
These two triangles are scaled copies of one another. The area of the smaller triangle is 9 square units. What is the area of the larger triangle? Explain or show how you know.
![Scaled copies of two triangles. Triangle on left, height = 3. Triangle on right, height = 6.](https://cms-im.s3.amazonaws.com/oQEvgYx2GEX898MTHKMnK5re?response-content-disposition=inline%3B%20filename%3D%227.1.A.PP.Image.44%25282%2529.png%22%3B%20filename%2A%3DUTF-8%27%277.1.A.PP.Image.44%25282%2529.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T163218Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=250e8e35f59b00d527e8a1b047529508df56d4b08dc0b8b3361f5f630eedfa3a)
Problem 5
Water costs $1.25 per bottle. At this rate, what is the cost of:
- 10 bottles?
- 20 bottles?
- 50 bottles?
Problem 6
The first row of the table shows the amount of dish detergent and water needed to make a soap solution.
-
Complete the table for 2, 3, and 4 batches.
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How much water and detergent is needed for 8 batches? Explain your reasoning.
number of batches | cups of water | cups of detergent |
---|---|---|
1 | 6 | 1 |
2 | ||
3 | ||
4 |