Lesson 12

Units in Scale Drawings

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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. 1 inch to 1 foot
  2. 1 inch to 100 feet
  3. 1 inch to 1 mile
  4. 1 centimeter to 1 meter
  5. 1 centimeter to 50 meters
  6. 1 centimeter to 1 kilometer

Solution

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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?

Solution

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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.

A:

0.75 cm to 1 km

B:

1 cm to 12 km

C:

6 mm to 2 km

D:

0.3 mm to 40 m

E:

1 inch to 7.62 km

Solution

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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. 

 

Solution

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Problem 5

Water costs $1.25 per bottle. At this rate, what is the cost of:

  1. 10 bottles?
  2. 20 bottles?
  3. 50 bottles?

Solution

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Problem 6

The first row of the table shows the amount of dish detergent and water needed to make a soap solution.

  1. Complete the table for 2, 3, and 4 batches.

  2. 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

Solution

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