To find the actual dimensions of Olivia's desk based on her drawing, we first need to convert the dimensions in the drawing from inches to feet using the scale provided, which states that 1/2 inch on the drawing equals 1 foot in reality.
Step 1: Convert Drawing Dimensions to Inches
-
The width of the drawing: \(1 \frac{1}{4}\) inches
- Convert this to an improper fraction: \[ 1 \frac{1}{4} = \frac{5}{4} \text{ inches} \]
-
The length of the drawing: \(2 \frac{1}{4}\) inches
- Convert this to an improper fraction: \[ 2 \frac{1}{4} = \frac{9}{4} \text{ inches} \]
Step 2: Scale Conversion Factor
Since \( \frac{1}{2} \) inch equals 1 foot, we can find out how many feet correspond to \(1\) inch: \[ 1 \text{ inch} = 2 \text{ feet} \]
Step 3: Calculate Actual Dimensions
-
Actual Width: \[ \text{Actual Width} = \frac{5}{4} \text{ inches} \times 2 \text{ feet/inch} = \frac{5}{4} \times 2 = \frac{10}{4} = 2.5 \text{ feet} \]
-
Actual Length: \[ \text{Actual Length} = \frac{9}{4} \text{ inches} \times 2 \text{ feet/inch} = \frac{9}{4} \times 2 = \frac{18}{4} = 4.5 \text{ feet} \]
Conclusion
The actual dimensions of Olivia's desk are:
- Width: 2.5 feet
- Length: 4.5 feet
1 answer