To determine the dimensions of the island on the blueprint, we first need to convert the actual dimensions of the island from feet to inches, and then apply the scale of the blueprint.
-
Convert the actual dimensions to feet in fractional form:
- Width: \( 2 \frac{5}{8} \) feet
- Length: \( 1 \frac{5}{16} \) feet
-
Convert these mixed numbers to improper fractions:
- Width: \[ 2 \times 8 + 5 = 16 + 5 = 21 \quad \Rightarrow \quad \frac{21}{8} \text{ feet} \]
- Length: \[ 1 \times 16 + 5 = 16 + 5 = 21 \quad \Rightarrow \quad \frac{21}{16} \text{ feet} \]
-
Convert the dimensions from feet to inches (1 foot = 12 inches):
- Width in inches: \[ \frac{21}{8} \text{ feet} \times 12 \text{ inches/foot} = \frac{21 \times 12}{8} = \frac{252}{8} = 31.5 \text{ inches} \]
- Length in inches: \[ \frac{21}{16} \text{ feet} \times 12 \text{ inches/foot} = \frac{21 \times 12}{16} = \frac{252}{16} = 15.75 \text{ inches} \]
-
Now, apply the scale of the blueprint (1 inch = 1.5 feet) to get the blueprint dimensions:
- Since 1 inch represents 1.5 feet, we divide the actual dimensions in inches by 1.5 to get the dimensions on the blueprint.
- Width on blueprint: \[ \frac{31.5 \text{ inches}}{1.5} = 21 \text{ inches} \]
- Length on blueprint: \[ \frac{15.75 \text{ inches}}{1.5} = 10.5 \text{ inches} \]
-
Final dimensions on the blueprint:
- Width: 21 inches
- Length: 10.5 inches
Therefore, the dimensions of the island on the blueprint are 21 inches by 10.5 inches.