Question

A scale drawing of a rectangular terrace at a resort is shown.

the rectangle is 18 on the bottom and 12 on the side. 1 inch equals 5 3/4 ft

What is the perimeter, in feet, of the actual terrace?
A.
60 feet
B.
83 feet
C.
172.5 feet
D.
345 feet

Answer 1

To find the perimeter of the actual terrace, we first need to determine the actual dimensions of the terrace in feet based on the scale provided.

The scale states that 1 inch equals 5.75 feet. The dimensions of the terrace on the drawing are:

- Length: 18 inches
- Width: 12 inches

Next, we will convert those dimensions from inches to feet.

### Calculate the actual dimensions:

1. **Length in feet:**
\[
\text{Actual Length} = 18 \text{ inches} \times 5.75 \text{ feet/inch} = 103.5 \text{ feet}
\]

2. **Width in feet:**
\[
\text{Actual Width} = 12 \text{ inches} \times 5.75 \text{ feet/inch} = 69 \text{ feet}
\]

### Calculate the perimeter:

The perimeter \(P\) of a rectangle is given by the formula:
\[
P = 2 \times (\text{Length} + \text{Width})
\]
Substituting the actual dimensions:
\[
P = 2 \times (103.5 + 69)
\]

Calculating inside the parentheses:
\[
103.5 + 69 = 172.5
\]

Now calculate the perimeter:
\[
P = 2 \times 172.5 = 345 \text{ feet}
\]

### Conclusion:

The perimeter of the actual terrace is \( \boxed{345} \) feet.