Similarity & Scale Problems - Pre Algebra

What does a scale of 1 : 100 on a drawing mean?

1 unit on the drawing represents 100 of the same units in reality.
In a scale written as a ratio without units, such as 1 : 50,000, what is true of the units?

Both parts use the same unit, so 1 cm on the map is 50,000 cm in reality, and 1 inch is 50,000 inches.
On a map, 2 inches represents 3 miles. Two landmarks are 4.5 inches apart on the map. How far apart are they?

6.75 miles. Each inch is 1.5 miles, and $4.5 \times 1.5 = 6.75$ .
A map has scale 1 : 50,000. Two points are 8 cm apart on the map. What is the actual distance in kilometers?

4 kilometers. $8 \times 50000 = 400000$ cm, and 100,000 cm is 1 km.
A model car is built at a scale of 1 : 24. The model is 7 inches long. How long is the real car in inches?

168 inches, since $7 \times 24 = 168$ .
A blueprint scale is 1 inch : 8 feet. A wall is 2.5 inches long on the blueprint. How long is the actual wall?

20 feet, since $2.5 \times 8 = 20$ .
A 6 ft person casts a 4 ft shadow. At the same time, a tree casts a 20 ft shadow. How tall is the tree?

30 feet. The triangles are similar, so $\frac{6}{4} = \frac{h}{20}$ gives $h = 30$ .
On a map, 3 cm represents 12 km. What is the scale written as 1 cm to a number of kilometers?

1 cm : 4 km, since $12 \div 3 = 4$ .
A map scale is 1 cm : 5 km. Two towns are 7 cm apart on the map. How far apart are they?

35 kilometers, since $7 \times 5 = 35$ .
A map scale is 1 inch : 15 miles. Two cities are 60 miles apart. How far apart are they on the map?

4 inches, since $60 \div 15 = 4$ .
A scale drawing has scale 1 : 20 for lengths. What is the ratio of an area on the drawing to the actual area?

$1 : 400$ . Areas scale by the square of the length ratio, and $20^2 = 400$ .
A 1 : 48 scale model of an airplane has a wingspan of 24 inches. What is the real wingspan in feet?

96 feet. The real wingspan is $24 \times 48 = 1152$ inches, and $1152 \div 12 = 96$ .

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