Solve Scale Drawing Problems - 7th Grade Math

1. What is the new perimeter if a figure with perimeter $14$ is enlarged by a length scale factor of $2$?

   $28$. Perimeter scales linearly: $14\times 2=28$.

2. What is the scale factor $k$ (drawing to actual) for the scale $3:12$?

   $k=\frac{1}{4}$. Simplify $\frac{3}{12}=\frac{1}{4}$ to find scale factor.

3. What is the new scale factor from original to new if you change from scale $1:50$ to scale $1:25$?

   $2$. New scale factor is $\frac{50}{25}=2$ (inverse ratio).

4. Which proportion correctly matches drawing $d$ and actual $a$ for scale $1\text{ cm}:4\text{ m}$?

   $\frac{d}{a}=\frac{1\text{ cm}}{4\text{ m}}$. Proportion sets up ratio of drawing to actual lengths.

5. What formula finds drawing length from actual length using scale factor $k$ (drawing to actual)?

   $\text{drawing} = \frac{\text{actual}}{k}$. Divide actual by scale factor to get drawing length.

6. What is the formula for actual length using drawing length $d$ and scale factor $k$?

   $\text{actual}=\frac{d}{k}$. Divide drawing length by scale factor to get actual size.

7. What formula finds actual length from drawing length using scale factor $k$ (drawing to actual)?

   $\text{actual} = k\times \text{drawing}$. Multiply drawing length by scale factor to get actual.

8. A figure is enlarged by length factor $k=4$. If the original area is $7\text{ cm}^2$, what is the new area?

   $112\text{ cm}^2$. Area scales by $k^2$: $7 \times 4^2 = 7 \times 16 = 112$.

9. What is the actual length if a segment is $6\text{ cm}$ on a drawing with scale $1\text{ cm}:4\text{ m}$?

   $24\text{ m}$. Multiply: $6\text{ cm} \times 4\text{ m/cm} = 24\text{ m}$.

10. What is the new drawing length if an original drawing length is $7\text{ cm}$ and the drawing is rescaled by a factor of $\frac{3}{2}$?

    $10.5\text{ cm}$. Multiply drawing length by rescale factor: $7\times\frac{3}{2}=10.5$.

11. What is the actual perimeter if a rectangle has drawing sides $4\text{ cm}$ and $7\text{ cm}$ with scale $1\text{ cm}:2\text{ m}$?

    $44\text{ m}$. Drawing perimeter is $2(4+7) = 22\text{ cm}$, multiply by scale factor $2$.

12. What is the scale factor from drawing to actual for the scale $1:50$?

    $50$. Scale factor equals the second number in the ratio.

13. What is the scale factor from actual to drawing for the scale $1:50$ (drawing:actual)?

    $\frac{1}{50}$. Reciprocal of scale factor converts from actual to drawing.

14. Identify the correct unit step: convert $3\text{ m}$ to centimeters.

    $300\text{ cm}$. Multiply meters by $100$ to convert to centimeters.

15. What is the perimeter scale factor from drawing to actual when the length scale factor is $k$?

    Actual perimeter $=$ drawing perimeter $\times k$. Perimeter scales linearly with the length scale factor.

16. Find the actual length in meters if the scale is $1:200$ and the drawing length is $4\text{ cm}$.

    $8\text{ m}$. Convert $800\text{ cm}$ to meters by dividing by $100$.

17. What is the area scale factor when a figure is enlarged by a length scale factor of $3$?

    $9$. Area scale factor equals $3^2=9$.

18. What is the new drawing length if a $5\text{ cm}$ segment is reproduced at a scale factor of $\frac{3}{2}$?

    $7.5\text{ cm}$. Multiply original length by new scale factor: $5 \times \frac{3}{2} = 7.5$.

19. A drawing is enlarged by scale factor $k=3$. If a segment is $4\text{ cm}$, what is the new length?

    $12\text{ cm}$. Multiply original length by scale factor: $4 \times 3 = 12$.

20. What does the scale $1\text{ cm}:5\text{ m}$ mean about drawing length and actual length?

    $1\text{ cm}$ on the drawing represents $5\text{ m}$ in real life. Scale shows ratio between drawing and real measurements.

21. A drawing rectangle is $3\text{ cm}$ by $5\text{ cm}$ at scale $1\text{ cm}:2\text{ m}$. What is actual area?

    $60\text{ m}^2$. Find actual dimensions $(6\text{ m} \times 10\text{ m})$, then multiply.

22. What does the scale $1\text{ cm}:4\text{ m}$ mean about drawing length and actual length?

    $1\text{ cm}$ on the drawing represents $4\text{ m}$ in real life. The scale shows the ratio between drawing and actual measurements.

23. What is the drawing length if the scale is $1\text{ in}:4\text{ ft}$ and the actual length is $12\text{ ft}$?

    $3\text{ in}$. Set up proportion: $\frac{1\text{ in}}{4\text{ ft}}=\frac{x}{12\text{ ft}}$.

24. Identify the correct area scale factor if the length scale factor is $k$ (drawing to actual).

    $k^2$. Area scales by the square of the length scale factor.

25. What is the drawing length if the actual length is $18\text{ m}$ and the scale is $1\text{ cm}:3\text{ m}$?

    $6\text{ cm}$. Divide: $18\text{ m} \div 3\text{ m/cm} = 6\text{ cm}$.

26. State the scale factor $k$ from drawing to actual for the scale $1:50$.

    $k=50$. Scale factor equals the denominator when scale is $1:n$.

27. Identify the missing value: scale $2\text{ cm}:5\text{ km}$, drawing $6\text{ cm}$ corresponds to what actual distance?

    $15\text{ km}$. Set up proportion: $\frac{2}{5} = \frac{6}{x}$, solve for $x = 15$.

28. What is the new area if a figure with area $12$ is reduced by a length scale factor of $\frac{1}{2}$?

    $3$. Area scales by $(\frac{1}{2})^2=\frac{1}{4}$: $12\times\frac{1}{4}=3$.

29. A drawing is reduced by scale factor $k=\frac{1}{2}$. If a segment is $10\text{ cm}$, what is the new length?

    $5\text{ cm}$. Multiply original length by scale factor: $10 \times \frac{1}{2} = 5$.

30. What is the actual area if the drawing area is $8\text{ cm}^2$ and the scale is $1\text{ cm}:5\text{ cm}$?

    $200\text{ cm}^2$. Area scale factor is $5^2 = 25$, so $8 \times 25 = 200$.

31. What is the formula for drawing length using actual length $a$ and scale factor $k$?

    $\text{drawing}=k\cdot a$. Multiply actual length by scale factor to get drawing size.

32. What does the scale $1:50$ mean in a scale drawing?

    $1$ unit on the drawing equals $50$ units in actual size. The ratio shows drawing units to actual units.

33. What is the drawing area if the actual area is $400\text{ m}^2$ and the scale is $1:10$ (drawing:actual)?

    $4\text{ m}^2$. Area scale factor is $10^2 = 100$, so $400 \div 100 = 4$.

34. What is the new area if a figure is reproduced with length scale factor $2$ and the original area is $9\text{ cm}^2$?

    $36\text{ cm}^2$. Area scales by $2^2 = 4$, so $9 \times 4 = 36$.

35. What is the drawing length if the actual length is $20\text{ m}$ and the scale is $1:5$?

    $4\text{ m}$. Divide $20\text{ m}\div 5=4\text{ m}$ using scale $1:5$.

36. Find the drawing length if the actual length is $18\text{ m}$ at scale $1\text{ cm}:3\text{ m}$.

    $6\text{ cm}$. Divide actual by scale ratio: $18 \div 3 = 6$.

37. What is the actual area if the drawing area is $12\text{ in}^2$ and the scale is $1\text{ in}:3\text{ ft}$?

    $108\text{ ft}^2$. Convert units: $3^2 = 9\text{ ft}^2/\text{in}^2$, so $12 \times 9 = 108$.

38. A map uses scale $1\text{ in}:10\text{ mi}$. Two cities are $2.5\text{ in}$ apart on the map. Find actual distance.

    $25\text{ mi}$. Multiply map distance by scale factor: $2.5 \times 10 = 25$.

39. What is the drawing area if the actual area is $200\text{ m}^2$ and the scale is $1:10$?

    $2\text{ m}^2$. Multiply by $(\frac{1}{10})^2=\frac{1}{100}$: $200\times\frac{1}{100}=2$.

40. Find the actual length if a drawing shows $6\text{ cm}$ at scale $1\text{ cm}:5\text{ m}$.

    $30\text{ m}$. Multiply drawing length by scale ratio: $6 \times 5 = 30$.

41. What is the formula for drawing area using actual area $A_a$ and length scale factor $k$?

    $A_{\text{drawing}}=k^2\cdot A_a$. Multiply actual area by $k^2$ since area scales quadratically.

42. What is the area scale factor from drawing to actual when the length scale factor is $k$?

    Actual area $=$ drawing area $\times k^2$. Area scales by the square of the linear scale factor.

43. Identify the missing value: scale $3\text{ in}:12\text{ ft}$, actual $20\text{ ft}$ corresponds to what drawing length?

    $5\text{ in}$. Set up proportion: $\frac{3}{12} = \frac{x}{20}$, solve for $x = 5$.

44. A drawing triangle has base $6\text{ cm}$ and height $4\text{ cm}$ at scale $1\text{ cm}:3\text{ m}$. What is actual area?

    $108\text{ m}^2$. Scale up dimensions, then use $A = \frac{1}{2}bh = \frac{1}{2}(18)(12)$.

45. State the scale factor $k$ from actual to drawing for the scale $1:50$.

    $k=\frac{1}{50}$. Reverse scale factor is the reciprocal of forward scale factor.

46. A blueprint uses $1\text{ cm}:0.5\text{ m}$. A wall is $7\text{ m}$ long. What length should it be on the blueprint?

    $14\text{ cm}$. Divide actual by scale ratio: $7 \div 0.5 = 14$.

47. What is the actual length for $7\text{ in}$ on a map with scale $1\text{ in}:12\text{ mi}$?

    $84\text{ mi}$. Multiply: $7\text{ in} \times 12\text{ mi/in} = 84\text{ mi}$.

48. What is the formula for actual area using drawing area $A_d$ and length scale factor $k$?

    $A_{\text{actual}}=\frac{A_d}{k^2}$. Divide drawing area by $k^2$ since area scales quadratically.

49. What is the drawing length for $90\text{ ft}$ actual if the scale is $1\text{ in}:15\text{ ft}$?

    $6\text{ in}$. Divide: $90\text{ ft} \div 15\text{ ft/in} = 6\text{ in}$.

50. What is the proportion to convert a drawing length $d$ to actual length $a$ using scale $1:n$?

    $\frac{d}{a}=\frac{1}{n}$. Set up proportion with drawing over actual equals scale ratio.

51. Which ratio represents the same scale as $2\text{ cm}:6\text{ m}$, written as $1\text{ cm}:\text{? m}$?

    $1\text{ cm}:3\text{ m}$. Simplify ratio by dividing both parts by $2$.

52. What is the definition of scale factor in a scale drawing?

    Scale factor $k=\frac{\text{drawing length}}{\text{actual length}}$. Ratio of drawing size to real-world size.

53. What is the new drawing length if a $12\text{ cm}$ segment is reproduced at a scale factor of $\frac{1}{3}$?

    $4\text{ cm}$. Multiply original length by new scale factor: $12 \times \frac{1}{3} = 4$.

54. A drawing polygon has perimeter $14\text{ cm}$ at scale $1\text{ cm}:4\text{ m}$. What is actual perimeter?

    $56\text{ m}$. Multiply drawing perimeter by scale factor: $14 \times 4 = 56$.

55. What is the area scale factor if the length scale factor is $k$?

    $k^2$. Area scales by the square of the length scale factor.

56. What is the actual length if the scale is $2\text{ cm}:5\text{ m}$ and the drawing length is $8\text{ cm}$?

    $20\text{ m}$. Set up proportion: $\frac{2\text{ cm}}{5\text{ m}}=\frac{8\text{ cm}}{x}$.

57. What is the actual length if a drawing length is $6\text{ cm}$ and the scale is $1:3$?

    $18\text{ cm}$. Multiply $6\text{ cm}\times 3=18\text{ cm}$ using scale $1:3$.

58. Find the actual length if the scale is $1:200$ and the drawing length is $4\text{ cm}$.

    $800\text{ cm}$. Multiply drawing by scale factor: $4 \times 200 = 800$.

59. What is the actual area if the drawing area is $36\text{ cm}^2$ and the length scale factor is $\frac{1}{3}$?

    $324\text{ cm}^2$. Divide by $(\frac{1}{3})^2=\frac{1}{9}$: $36\div\frac{1}{9}=324$.

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