Question

a model of a skyscraper was made by an architect. the model was 10 in. high. if the architect used a scale of 2 inches represents 12 feet, what would be the actual height of the building?
a 60 ft
b 240 ft
c 120 ft
d 12 ft

Explanation:

Step1: Find scale factor per inch

First, find how many feet 1 inch represents. Given 2 inches = 12 feet, so 1 inch represents $\frac{12}{2} = 6$ feet.

Step2: Calculate actual height

The model is 10 inches high. So actual height is $10 \times 6 = 60$ feet? Wait, no, wait. Wait, 2 inches is 12 feet, so the ratio of model to actual is 2 inches : 12 feet, which simplifies to 1 inch : 6 feet. Wait, but 10 inches model. Wait, let's set up a proportion. Let $x$ be the actual height. Then $\frac{2}{12} = \frac{10}{x}$. Cross - multiply: $2x = 12\times10$, $2x = 120$, $x=\frac{120}{2}=60$? Wait, no, wait, 2 inches represents 12 feet, so 1 inch represents 6 feet. So 10 inches would be 106 = 60 feet? Wait, but let's check again. Wait, 2 inches is 12 feet, so the scale is 2 in : 12 ft, so the ratio of model to real is 2:12, which is 1:6 (inches to feet). So 10 inches model: 106 = 60 feet. So the answer should be 60 ft. Wait, but let's do the proportion correctly. Let model height be $m$ and actual height be $a$. The scale is $m:a = 2\mathrm{in}:12\mathrm{ft}$. We have $m = 10\mathrm{in}$, so $\frac{2}{12}=\frac{10}{a}$. Cross - multiply: $2a=12\times10$, $2a = 120$, $a = 60$. So yes, 60 feet.

Answer:

A. 60 ft