Question

above are two different models of the same rectangular hallway. if the length of the model on the top is 6 cm, what is the length of the model on the bottom?
1 cm = 18 ft
1 cm = 3 ft
a. 36 cm
b. 15 cm
c. 12 cm
d. 21 cm

Explanation:

Step1: Find actual length from top model

The top model has a scale of \(1\,\text{cm} = 18\,\text{ft}\) and length \(6\,\text{cm}\). So actual length \(= 6\times18 = 108\,\text{ft}\).

Step2: Find length on bottom model

The bottom model has a scale of \(1\,\text{cm} = 3\,\text{ft}\). To find the length on the bottom model, divide actual length by 3: \(\frac{108}{3}= 36\,\text{cm}\)? Wait, no, wait. Wait, maybe I mixed up. Wait, no, the top model's length is 6 cm with scale 1 cm = 18 ft, so actual length is \(6\times18 = 108\) ft. Then the bottom model has scale 1 cm = 3 ft, so the length on bottom model is \(\frac{108}{3}= 36\)? Wait, but the options have 36 as A. Wait, but let me check again. Wait, maybe the top model is the small rectangle, and the bottom is the large one. Wait, the problem says "two different models of the same rectangular hallway". So the actual length is the same. Top model: length 6 cm, scale 1 cm = 18 ft. So actual length \(L = 6\times18 = 108\) ft. Bottom model: scale 1 cm = 3 ft. So length on bottom model \(l=\frac{L}{3}=\frac{108}{3}= 36\) cm? But wait, the options have A as 36 cm. Wait, but maybe I made a mistake. Wait, no, let's re-express.

Wait, maybe the top model's scale is 1 cm = 18 ft, so 1 cm on top is 18 ft. The bottom model's scale is 1 cm = 3 ft, so 1 cm on bottom is 3 ft. So the ratio of scales: top scale factor is 18 ft/cm, bottom is 3 ft/cm. So the length on bottom model is (length on top model) × (top scale / bottom scale). So \(6\,\text{cm}\times\frac{18\,\text{ft/cm}}{3\,\text{ft/cm}} = 6\times6 = 36\,\text{cm}\). Yes, that makes sense. So the length on the bottom model is 36 cm.

Answer:

A. 36 cm