A scale drawing of a new building has `1/2` inch representing 40 feet . If a conference room has a floor length of 60 feet , what is the floor length , in inches , on the scale drawing ?

Options

A. `3/4`
B. `7/8`
C. 1
D. `1 1/2`

Answer

To find the floor length of the conference room in inches on the scale drawing, we can follow these steps:

### Step 1: Understand the scale
The scale given is \( \frac{1}{2} \) inch represents 40 feet.

### Step 2: Determine how many feet are represented by 1 inch
Since \( \frac{1}{2} \) inch represents 40 feet, we can find out how many feet are represented by 1 inch by doubling this value:
\[ 1 \text{ inch} = 2 \times 40 \text{ feet} = 80 \text{ feet} \]

### Step 3: Set up the proportion for the conference room
The conference room has a floor length of 60 feet. We need to find out how many inches this length represents on the scale drawing. Since we know that 1 inch represents 80 feet, we can set up the following proportion:
\[ \text{Length in inches} = \frac{\text{Actual length in feet}}{\text{Feet per inch}} = \frac{60 \text{ feet}}{80 \text{ feet/inch}} \]

### Step 4: Calculate the length in inches
Now we can perform the calculation:
\[ \text{Length in inches} = \frac{60}{80} = \frac{3}{4} \text{ inch} \]

### Final Answer
The floor length of the conference room on the scale drawing is \( \frac{3}{4} \) inch.

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