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, we need to use the concept of proportionality. The idea is to find the ratio between Lady Gaga’s actual height and her arm length, and then apply that ratio to the scaled-down version of her height.
Step 1: Determine the ratio of height to arm length.
Lady Gaga’s actual height is 5 feet 3 inches, which is equal to 63 inches (since 1 foot = 12 inches).
- Height = 63 inches
- Arm length = 24 inches
Now, the ratio of height to arm length is:Ratio=HeightArm length=6324\text{Ratio} = \frac{\text{Height}}{\text{Arm length}} = \frac{63}{24}Ratio=Arm lengthHeight=2463
Simplifying this fraction:6324=2.625\frac{63}{24} = 2.6252463=2.625
Step 2: Apply the ratio to the scaled height.
Gaga wants her scaled drawing to be 10 inches tall. So, now we need to find out how long her arm should be in the scaled drawing, using the same ratio:
Let x represent the length of the arm in the drawing. The ratio of the height to the arm length should be the same, so:10x=2.625\frac{10}{x} = 2.625×10=2.625
Step 3: Solve for x.
To find x, multiply both sides of the equation by x:10=2.625×x10 = 2.625 \times x10=2.625×x
Now divide both sides by 2.625:x=102.625=3.81 inchesx = \frac{10}{2.625} = 3.81 \, \text{inches}x=2.62510=3.81inches
Final Answer:
So, Lady Gaga should draw her arm 3.81 inches long.
Explanation:
By setting up the ratio between her height and arm length, we can scale it down proportionally to keep the correct proportions in the drawing. This ensures that the arm length in the drawing is representative of the actual arm length, just reduced in size to match her desired 10-inch tall figure.
