Testinar Grade 7 math

Reproducing Scale Drawings at a Different Scale

Students will build Grade 7 mastery of reproducing scale drawings at a different scale using models, equations, and test-style reasoning.

CH06-02 Geometry and Scale
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. 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?

    1. \(1\) in by \(1.5\) in
    2. \(2\) in by \(3\) in
    3. \(8\) in by \(12\) in
    4. \(16\) in by \(24\) in

  2. 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?

    1. \(3\) m by \(5\) m
    2. \(300\) cm by \(500\) cm
    3. \(1\) m by \(1.67\) m
    4. \(6\) m by \(10\) m

  3. 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?

    1. \(13\) ft
    2. \(40\) ft
    3. \(45\) ft
    4. \(64\) ft

  4. A rectangle on a map has length \(7\) cm and width \(4\) cm. The map scale is \(1\) cm \(:2\) km. When the map is enlarged so that the new scale becomes \(1\) cm \(:1\) km, what are the new dimensions?

    1. \(7\) cm by \(4\) cm
    2. \(14\) cm by \(8\) cm
    3. \(3.5\) cm by \(2\) cm
    4. \(3\) cm by \(2\) cm

  5. 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?

    1. \(25\) ft by \(35\) ft
    2. \(2.5\) ft by \(3.5\) ft
    3. \(12.5\) ft by \(17.5\) ft
    4. \(20\) ft by \(28\) ft

  6. 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?

    1. \(3\) cm
    2. \(6\) cm
    3. \(12\) cm
    4. \(24\) cm

  7. A blueprint of a house wing shows a rectangular area \(5\) cm by \(7\) cm at scale \(1\) cm \(:3\) m. A new blueprint is drawn at scale \(1\) cm \(:6\) m. What are the dimensions on the new blueprint?

    1. \(2.5\) cm by \(3.5\) cm
    2. \(5\) cm by \(7\) cm
    3. \(10\) cm by \(14\) cm
    4. \(15\) cm by \(21\) cm

  8. A landscape drawing shows a rectangular flower bed \(8\) inches by \(12\) inches at scale \(1\) in \(:2\) ft. What are the dimensions of the actual flower bed?

    1. \(2\) ft by \(3\) ft
    2. \(4\) ft by \(6\) ft
    3. \(16\) ft by \(24\) ft
    4. \(32\) ft by \(48\) ft
Teacher and parent reference

Answer key and explanations

  1. B. \(2\) in by \(3\) in

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

  2. A. \(3\) m by \(5\) m

    Scale 1 cm : 1 m means 1 cm on the drawing represents 1 m in reality. Scale factor is 1 m per cm. 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. This foundational skill (single scale) is the basis for comparing two scales in later problems.

  3. B. \(40\) ft

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

  4. B. \(14\) cm by \(8\) cm

    Original scale 1:2 means 1 cm = 2 km. New scale 1:1 means 1 cm = 1 km. The real-world distance per cm is halved, so the drawing must double in size. Scale factor ratio: \(1 \div 2 = 0.5\), reciprocal shrink \(= 2\). New dimensions: \(7 \times 2 = 14\) cm and \(4 \times 2 = 8\) cm.

  5. A. \(25\) ft by \(35\) ft

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

  6. A. \(3\) cm

    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).

  7. A. \(2.5\) cm by \(3.5\) cm

    Original scale 1:3 means 1 cm = 3 m. New scale 1:6 means 1 cm = 6 m. Real-world distance per cm doubled (3 to 6), so drawing shrinks by factor \(3 \div 6 = 0.5\) (or multiply by reciprocal 6 รท 3 = 2, then invert: 1/2). New dimensions: \(5 \div 2 = 2.5\) cm and \(7 \div 2 = 3.5\) cm.

  8. C. \(16\) ft by \(24\) ft

    Multiply by scale factor: \(8 \text{ in} \times 2 \text{ ft/in} = 16\) ft and \(12 \times 2 = 24\) ft.

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