Grade 7 Reproducing Scale Drawings at a Different Scale

Visual Model 1

Question: Two drawings of the same rectangular room are shown. If Drawing A uses scale \(1\) in \(:4\) ft and is \(3 \times 2\) in, what is the scale of Drawing B if it shows \(1.5 \times 1\) in?

• A. \(1\) in \(:2\) ft
• B. \(1\) in \(:8\) ft
• C. \(1\) in \(:4\) ft
• D. \(2\) in \(:1\) ft

Why it works: Drawing A: actual room is \(3 \times 4 = 12\) ft by \(2 \times 4 = 8\) ft. Drawing B at \(1.5 \times 1\) in for same room: scale is \(12 \div 1.5 = 8\) ft per inch, or \(1\) in \(:8\) ft.

Answer: \(1\) in \(:8\) ft

Visual Model 2

Question: A scale drawing of a rectangular room is \(8\) cm \(\times\) \(4.8\) cm. The drawing is enlarged proportionally so the new dimensions are \(10\) cm \(\times\) \(6\) cm. If the original scale was \(1\) cm \(:5\) m, what is the scale of the enlarged drawing?

• A. \(1\) cm \(:4\) m
• B. \(1\) cm \(:6.25\) m
• C. \(1\) cm \(:3.125\) m
• D. \(1\) cm \(:2.5\) m

Why it works: Zoom ratio: \(10 / 8 = 1.25\). Drawing is enlarged by 1.25 times, so the new scale is \(5 \text{ m} / 1.25 = 4\) m per cm, or \(1\) cm \(:4\) m.

Answer: \(1\) cm \(:4\) m

Example 1

Question: A rectangle has dimensions \(4\) in by \(6\) in at a scale of \(1\) in \(:2\) ft. If redrawn at a new scale of \(1\) in \(:4\) ft, what are the new dimensions?

• A. \(1\) in by \(1.5\) in
• B. \(2\) in by \(3\) in
• C. \(8\) in by \(12\) in
• D. \(16\) in by \(24\) in

1. At scale 1:2, the drawing is \(4 \times 6\) in representing a fixed real object.
2. At scale 1:4, the same object is represented differently.
3. The ratio of real-world per drawing unit goes from 2 to 4 (doubled), so the drawing must shrink by factor \(4 \div 2 = 2\).
4. New dimensions: \(4 \div 2 = 2\) in and \(6 \div 2 = 3\) in.

Answer: \(2\) in by \(3\) in

Example 2

Question: A blueprint shows a room measuring \(3\) cm by \(5\) cm at a scale of \(1\) cm \(:1\) m. What are the actual room dimensions?

• A. \(3\) m by \(5\) m
• B. \(300\) cm by \(500\) cm
• C. \(1\) m by \(1.67\) m
• D. \(6\) m by \(10\) m

1. Scale 1 cm : 1 m means 1 cm on the drawing represents 1 m in reality.
2. Scale factor is 1 m per cm.
3. Multiply each drawing dimension by the scale factor: \(3 \text{ cm} \times 1 \text{ m/cm} = 3\) m and \(5 \text{ cm} \times 1 \text{ m/cm} = 5\) m.
4. This foundational skill (single scale) is the basis for comparing two scales in later problems.

Answer: \(3\) m by \(5\) m

Example 3

Question: A scale model of a car is drawn at a scale of \(1\) in \(:5\) ft. If the model is \(8\) inches long, what is the length of the actual car?

• A. \(13\) ft
• B. \(40\) ft
• C. \(45\) ft
• D. \(64\) ft

1. Scale 1 in : 5 ft means 1 inch on the model represents 5 feet in reality.
2. Scale factor is 5 ft per inch.
3. To find actual length, multiply: \(8 \text{ in} \times 5 \text{ ft/in} = 40\) ft.
4. The scale factor (5 ft/in) is the key ratio that converts drawing dimensions to real-world dimensions.

Answer: \(40\) ft

Problem 1

Question: A floor plan shows a rectangular office that is \(2.5\) inches by \(3.5\) inches at a scale of \(1\) in \(:10\) ft. Which pair of measurements are the actual office dimensions?

• A. \(25\) ft by \(35\) ft
• B. \(2.5\) ft by \(3.5\) ft
• C. \(12.5\) ft by \(17.5\) ft
• D. \(20\) ft by \(28\) ft

Why it works: Multiply drawing dimensions by scale factor: \(2.5 \times 10 = 25\) ft and \(3.5 \times 10 = 35\) ft.

Answer: \(25\) ft by \(35\) ft

Problem 2

Question: A scale drawing of a rectangular garden is \(6\) cm long at a scale of \(1\) cm \(:0.5\) m. If the scale is changed to \(1\) cm \(:1\) m, what will be the new length?

• A. \(3\) cm
• B. \(6\) cm
• C. \(12\) cm
• D. \(24\) cm

Why it works: Original scale 1:0.5 means 1 cm = 0.5 m. New scale 1:1 means 1 cm = 1 m. Real-world distance per cm doubled (0.5 to 1), so the drawing shrinks. Scale factor ratio: \(1 \div 0.5 = 2\), so drawing shrinks by factor \(1 \div 2 = 0.5\). New length: \(6 \times 0.5 = 3\) cm (or \(6 \div 2 = 3\) cm).

Answer: \(3\) cm