A scale drawing uses a scale of \(1\) cm \(:4\) m. In the drawing, a wall is \(7\) cm long. What is the actual length of the wall?
- \(3\) m
- \(11\) m
- \(28\) m
- \(32\) m
Testinar Grade 7 math
Understanding and Using Scale Drawings
Students will build Grade 7 mastery of understanding and using scale drawings using models, equations, and test-style reasoning.
CH06-01
Geometry and Scale
- Name
- Date
- Score
- ____ / 8
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A map uses a scale of \(1\) inch \(:50\) miles. Two cities are \(3\) inches apart on the map. What is the actual distance between the cities?
- \(100\) miles
- \(150\) miles
- \(200\) miles
- \(250\) miles
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A scale drawing has a scale of \(1\) cm \(:2\) m. If an actual room is \(8\) m wide, how wide is it in the drawing?
- \(2\) cm
- \(4\) cm
- \(6\) cm
- \(8\) cm
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Which scale would make the drawing larger than the actual object?
- \(1\) in \(:10\) ft
- \(1\) in \(:5\) ft
- \(2\) in \(:1\) ft
- \(1\) in \(:100\) ft
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A blueprint uses a scale of \(\frac{1}{4}\) inch \(:1\) foot. A door in the blueprint is \(\frac{3}{4}\) inch tall. What is the actual height of the door?
- \(1\) foot
- \(2\) feet
- \(3\) feet
- \(4\) feet
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A scale drawing has a scale of \(1\) cm \(:5\) cm. What is the scale factor?
- \(1\)
- \(2\)
- \(5\)
- \(10\)
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A map has a scale of \(2\) cm \(:3\) km. If two towns are \(10\) cm apart on the map, how far apart are they in reality?
- \(12\) km
- \(15\) km
- \(18\) km
- \(20\) km
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A scale drawing shows a rectangular room with dimensions \(5\) cm \(\times 3\) cm. The scale is \(1\) cm \(:3\) m. What is the area of the actual room in square meters?
- \(15\) m\(^2\)
- \(45\) m\(^2\)
- \(135\) m\(^2\)
- \(225\) m\(^2\)
Answer key and explanations
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C. \(28\) m
Multiply the drawing length by the scale: \(7\times4=28\) m.
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B. \(150\) miles
Multiply the map distance by the scale factor: \(3 \times 50 = 150\) miles.
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B. \(4\) cm
Divide actual length by scale factor: \(8 \div 2 = 4\) cm.
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C. \(2\) in \(:1\) ft
In scale \(2 \text{ in}:1 \text{ ft}\), one foot in reality becomes \(2\) inches in the drawing, making the drawing larger than the object. All others make the drawing smaller.
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C. \(3\) feet
If \(\frac{1}{4}\) inch represents \(1\) foot, then \(\frac{3}{4}\) inch represents \(3\) feet: \(\frac{3}{4} \div \frac{1}{4} = 3\).
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C. \(5\)
The scale factor is the ratio of actual to drawing: \(5 \text{ cm} \div 1 \text{ cm} = 5\). Each unit on the drawing represents \(5\) times that length in reality.
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B. \(15\) km
Set up the ratio: \(\frac{2 \text{ cm}}{3 \text{ km}} = \frac{10 \text{ cm}}{x}\). Cross-multiply: \(2x = 30\), so \(x = 15\) km.
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C. \(135\) m\(^2\)
Actual dimensions: \(15\) m \(\times 9\) m. The scale factor is \(3\) (linear), so area scale is \(3^2 = 9\). Drawing area: \(5 \times 3 = 15\) cm\(^2\). Actual area: \(15 \times 9 = 135\) m\(^2\).
