Lesson 12

Units in Scale Drawings

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

For access, consult one of our IM Certified Partners.

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

For access, consult one of our IM Certified Partners.

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

For access, consult one of our IM Certified Partners.

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.

Solution

For access, consult one of our IM Certified Partners.

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

For access, consult one of our IM Certified Partners.

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

For access, consult one of our IM Certified Partners.