Question

The blueprint for Zahra’s new office measures `4` cm long and `2` cm wide.

The scale for the blueprint is `6` cm to `15` ft.
What is the actual area of her office?

Answer 1

Answer: 20 ft^2

Explanation:

15 ft:6 cm = x: 4*2 cm^2

15 ft:6 cm = x: 8 cm^2

15/6=x/8

15*8/6=x

x=120/6

x=20 ft^2

Answer 2

1. The actual length is
`\(4 \text{ cm} * 2.5 \text{ ft/cm} = 10 \text{ ft}\).`

2. The actual width is
`\(2 \text{ cm} * 2.5 \text{ ft/cm} = 5 \text{ ft}\).`

3. The actual area is
`\(10 \text{ ft} * 5 \text{ ft} = 50.0 \text{ ft}^2\).`

To find the actual area of Zahra's office based on the blueprint and scale, we need to follow these steps:

1. Convert the blueprint dimensions to the actual dimensions using the scale.

2. Calculate the area using the actual dimensions.

Given:

- The blueprint dimensions are
`\(4 \text{ cm}\)` by
`\(2 \text{ cm}\).`

- The scale is
`\(6 \text{ cm}\)` (on the blueprint) to
`\(15 \text{ ft}\)` (in reality).

Step 1: Convert blueprint dimensions to actual dimensions

First, we'll find the conversion factor from cm to ft using the scale:

`\[ \frac{15 \text{ ft}}{6 \text{ cm}} = \frac{2.5 \text{ ft}}{1 \text{ cm}} \]`

Now, we apply this conversion factor to the blueprint dimensions:

- Actual length =
`\(4 \text{ cm} * \frac{2.5 \text{ ft}}{1 \text{ cm}}\)`

- Actual width =
`\(2 \text{ cm} * \frac{2.5 \text{ ft}}{1 \text{ cm}}\)`

Step 2: Calculate the actual area

- The area in square feet will be the actual length times the actual width.

Let's perform the calculations.

The actual area of Zahra's office, based on the blueprint and scale provided, is
`\(50.0\)` square feet. Here's the step-by-step calculation:

1. The actual length is
`\(4 \text{ cm} * 2.5 \text{ ft/cm} = 10 \text{ ft}\).`

2. The actual width is
`\(2 \text{ cm} * 2.5 \text{ ft/cm} = 5 \text{ ft}\).`

3. The actual area is
`\(10 \text{ ft} * 5 \text{ ft} = 50.0 \text{ ft}^2\).`