Lady Gaga wants to make a scale drawing of herself in her meat dress standing straight with her arms down. Gaga is 5 feet 3 inches tall. Her arm is 24 inches long. If Gaga want to make a drawing of herself 10 inches tall, then how long should she draw her arm?
The Correct Answer and Explanation is:
To solve this problem, we need to use the concept of proportionality because the height of Lady Gaga and her arm length should be scaled down in the same ratio.
Step 1: Find the ratio of the drawing’s height to Gaga’s actual height.
Gaga’s actual height is 5 feet 3 inches. To convert this to inches:
- 5 feet = 5 × 12 = 60 inches.
- Therefore, her total height in inches is 60 + 3 = 63 inches.
Now, the height of the drawing is given as 10 inches. The ratio of the drawing’s height to Gaga’s actual height is:Ratio=Drawing heightActual height=10 inches63 inches=1063.\text{Ratio} = \frac{\text{Drawing height}}{\text{Actual height}} = \frac{10 \text{ inches}}{63 \text{ inches}} = \frac{10}{63}.Ratio=Actual heightDrawing height=63 inches10 inches=6310.
Step 2: Find the length of Gaga’s arm in the drawing.
Gaga’s actual arm length is 24 inches. To find the corresponding arm length in the drawing, we multiply the actual arm length by the ratio:Arm length in drawing=24×1063.\text{Arm length in drawing} = 24 \times \frac{10}{63}.Arm length in drawing=24×6310.Arm length in drawing=24063≈3.81 inches.\text{Arm length in drawing} = \frac{240}{63} \approx 3.81 \text{ inches}.Arm length in drawing=63240≈3.81 inches.
Final Answer:
Lady Gaga should draw her arm approximately 3.81 inches long in the scaled-down version of the drawing.
Explanation:
By maintaining the same proportionality for the height and arm length, we ensure that the drawing retains the correct proportions of Lady Gaga’s body and arm. The ratio method allows us to scale both her height and arm length consistently without distorting the body proportions.
