# Scale Factors (Grade 7)

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## Scale Factors

1.

Manny drew a scale diagram of his classroom. His real classroom is 20 feet wide. Manny's drawing is 4 centimeters (cm) wide. What is the scale factor of the drawing?

- 1 cm = 4 feet
- 1 cm = 5 feet
- 1 cm = 20 feet
- 1 cm = 80 feet

2.

A map has a scale of 1 inch equals 0.5 mile. The map distance from Goffstown to Brooksville is 7 inches. How many miles is it from Goffstown to Brooksville?

- 3.5 miles
- 7.0 miles
- 7.5 miles
- 14.0 miles

3.

Triangle ABC has side lengths with a ratio of 3:4:5. Similar triangle XYZ has a scale factor of 2 compared to triangle ABC. Which of the following could be side lengths of triangle XYZ?

- 1 cm, 2 cm, 3 cm
- 5 cm, 6 cm, 7 cm
- 4 cm, 8 cm, 12 cm
- 6 cm, 8 cm, 10 cm

4.

The perimeter of a regular hexagon is 48. If the side length of a similar hexagon is 3 times that of the original hexagon, which statement is true about the similar hexagon?

- The perimeter of the similar hexagon is 3 times the perimeter of the original hexagon.
- The perimeter of the similar hexagon is 8 times the perimeter of the original hexagon.
- The perimeter of the similar hexagon is 11 times the perimeter of the original hexagon.
- The perimeter of the similar hexagon is 24 times the perimeter of the original hexagon.

5.

The length of each side of a square is 5 meters. If the lengths of the sides of the square are doubled, which statement is true about the new area of the square?

- The new area is 2 times the old area.
- The new area is 4 times the old area.
- The new area is 5 times the old area.
- The new area is 10 times the old area.

6.

Kallie scans a photo that is 5 in. wide by 7 in. long into his computer. If he scales the length down to 3.5 in., how wide should the similar photo be?

7.

A telephone pole casts an 80 ft shadow, while a 3.5 ft child standing nearby casts a 6 ft shadow. How tall is the pole?

8.

Penny is making a model of a Ferris wheel that is 60 feet tall. The model is 15 inches tall. Penny is also making a model of the sky needle ride that is 100 feet tall using the same scale. How tall is the model of the sky needle?

9.

The rectangle has the following dimensions: length=6 in, width=4 in. If the figure was dilated by a scale factor of two, then what is the perimeter of the new figure? Write a ratio to compare the perimeter of the new figure to the perimeter of the old figure. What is significant about the ratio?

10.

Given the figure shown, assign the following measures: AB = 4, BC = 7, CA = 8. Now use a scale factor of 1/2 to draw a similar figure (show labels). Make markings on both triangles to indicate all corresponding sides and angles.

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