To find the length of Janie's miniature couch for the dollhouse, we need to use the scale provided, which is 1 inch : 2 feet.
First, we convert the length of Janie's actual couch from feet to inches. Since 1 foot equals 12 inches, we calculate:
\[ 7 \frac{1}{2} \text{ feet} = 7.5 \text{ feet} = 7.5 \times 12 \text{ inches} = 90 \text{ inches} \]
Next, we use the scale to figure out how long the miniature couch should be. According to the scale, 2 feet equals 1 inch. Therefore, we convert the length of the actual couch into the scale length:
\[ \text{Length in inches} = \frac{\text{Length in feet}}{2} = \frac{7.5 \text{ feet}}{2} = 3.75 \text{ inches} \]
Finally, we can express \( 3.75 \text{ inches} \) in fractional form:
\[ 3.75 = 3 \frac{3}{4} \]
So the length of the miniature couch for the dollhouse is \( \mathbf{3 \frac{3}{4}} \) inches.
The correct answer is:
D. 3 3/4