Question

Construction In a blueprint, 1 inch represents an actual length of 13 feet. If the dimensions of a kitchen on the blueprint are \(1.25\) inches by \(0.75\) inch, what are the actual dimensions?

Short answer

The actual dimensions are 16.25 feet by 9.75 feet.

Step-by-step solution

Understand the Scale

The blueprint scale is given as 1 inch representing 13 feet. This means that every inch on the blueprint corresponds to 13 actual feet.

Convert Lengths Using the Scale

We need to convert the blueprint dimensions into actual dimensions using the scale factor. To find the actual dimension in feet of a 1.25-inch length on the blueprint, multiply 1.25 by 13.

Calculate the Actual Length of 1.25-inch Side

\[\text{Actual length of longer side} = 1.25 \times 13 = 16.25 \text{ feet}\]

Calculate the Actual Length of 0.75-inch Side

Next, calculate the actual dimension for the 0.75-inch side by multiplying it by 13: \[\text{Actual length of shorter side} = 0.75 \times 13 = 9.75 \text{ feet}\]

Provide the Final Answer

The actual dimensions of the kitchen are 16.25 feet by 9.75 feet, corresponding to the blueprint dimensions of 1.25 inches by 0.75 inches.

Key concepts

Blueprint interpretation

When we talk about blueprints, we are looking at scaled-down representations of actual spaces or constructions. This means that something large, like a building or a room, is shrunk down to a manageable size on paper. Blueprints are essential in construction because they communicate the design and dimensions of a building to engineers, builders, and clients. Interpreting a blueprint requires understanding the scale it is drawn at, which tells you how the measurements on the paper relate to real-world measurements.
The blueprint in our example uses a scale where 1 inch on paper represents 13 feet in reality. That is crucial for accurately transferring what is on paper into real life without errors.

• Scales simplify large measurements, making them easy to visualize and work with.
• They ensure everyone involved has the same understanding of size and distance.
• Blueprints with precise scales mean precise construction, avoiding costly mistakes.

By comprehending blueprints and their scales, we ensure that the actual construction matches the intended design.

Scale factor conversion

Scale conversion helps in translating measures on a blueprint to their real-world sizes. In our exercise, the scale factor is the ratio between the measurement on the blueprint and the actual measurement: 1 inch equals 13 feet.
To use a scale factor effectively, you multiply the blueprint measurement by the scale. This gives you the corresponding real-world size.
For instance:

• To convert 1.25 inches from the blueprint, we multiply 1.25 by the scale factor 13, to get the actual length of 16.25 feet.
• Similarly, 0.75 inches multiplied by 13 gives 9.75 feet for the shorter side.

Understanding and applying scale factors is fundamental for builders and architects. It ensures blueprints accurately reflect dimensions and prevents critical errors in construction.

Measurement in construction

Measurements play a fundamental role in construction as they ensure precision and accuracy in building projects. Whether dealing with large structures or small details, precise measurements matter.

• Accurate measurement conversions from blueprints help builders create structures exactly as planned.
• Consistent measurement practices foster clear communication among architects, builders, and clients.

In the context of our exercise, we converted the blueprint dimensions, stepping from a small scale on paper to real-world measurements. This requires both an understanding of scale conversions and careful calculation to maintain accuracy. Every inch and foot measured and converted correctly contributes to the project's success and helps avoid expensive mistakes during the build. When correct conversion practices are applied, as in our example exercise, the final construction will meet the intended specifications.