Question

The figure shows a scale drawing of an office floor plan on graph paper.

The grid showing a figure is composed of 4 by 4 square, 3 by 2 rectangle, and 5 by 3 rectangle. The key shows 1 unit equals three and a half feet.

What is the actual perimeter of the office?
A.
112 feet

B.
119 feet

C.
129.5 feet

D.
147 feet

Answer 1

To find the actual perimeter of the office, we need to calculate the perimeter of the scale drawing first and then convert it using the given scale.

Let's break down the dimensions based on the shapes you mentioned on the graph paper:

1. **4 by 4 square**: The perimeter \( P \) of a square is given by the formula \( P = 4 \times \text{side length} \).
- Side length = 4 units
- Thus, perimeter = \( 4 \times 4 = 16 \) units

2. **3 by 2 rectangle**: The perimeter of a rectangle is calculated with \( P = 2 \times (\text{length} + \text{width}) \).
- Length = 3 units, Width = 2 units
- Thus, perimeter = \( 2 \times (3 + 2) = 2 \times 5 = 10 \) units

3. **5 by 3 rectangle**: Using the same formula for the perimeter:
- Length = 5 units, Width = 3 units
- Thus, perimeter = \( 2 \times (5 + 3) = 2 \times 8 = 16 \) units

Now we need to sum the perimeters of these shapes for the total perimeter of the office layout. However, if these shapes are adjacent to each other in the drawing, some sides may not be included in the total perimeter count, since they are shared.

Assuming we're calculating the total bounding perimeter, and not accounting for overlapping sides, you would simply sum the individual perimeter figures:

Total perimeter (in units) = \( 16 + 10 + 16 = 42 \) units.

Next, we convert the units to feet using the given scale where 1 unit equals 3.5 feet:

Actual perimeter = Total perimeter × Scale factor
Actual perimeter = \( 42 \times 3.5 \) feet.

Calculating this:

\[
42 \times 3.5 = 147 \text{ feet}
\]

Thus, the actual perimeter of the office is:

**D. 147 feet**