Lesson 12: Practice Problems

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 -inch-by--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

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.

  1. 0.75 cm to 1 km

  2. 1 cm to 12 km

  3. 6 mm to 2 km

  4. 0.3 mm to 40 m

  5. 1 inch to 7.62 km

Problem 4 From Unit 1 Lesson 6

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.

Small triangle has a height of 3. Large triangle has a height of 6.

Problem 5 From Unit 2 Lesson 8

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

  1. 10 bottles?

  2. 20 bottles?

  3. 50 bottles?

Problem 6 From Unit 2 Lesson 11

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.

    number of batches

    cups of water

    cups of detergent

  2. How much water and detergent is needed for 8 batches? Explain your reasoning.