Before a new building is constructed, an architect is hired to draw up plans for the structure. If the building will be very large or complex, and therefore expensive, the architect will build a small model to help the client visualize the final product. It is vitally important that this planning process is done well so that the new building is not only pleasing to the eye, but also safe and functional. Study these examples of how proportions and ratios are used to design a home.
Drawing to Scale
From Plans to Building
The plans drawn up by architects allow a construction company to start building. To make sense of the document, though, the various members of the construction crew need to know the scale in which the plans are drawn. Each inch on the blueprint or drawing represents a certain number of feet for the actual building.
Suppose the scale for a particular blueprint is three inches to one real-life foot of building space. If you know this ratio, you can then figure out from the drawing the dimensions of the actual building. How would you write the ratio of inches to feet? Click the Answer Button below to see if you pictured this ratio correctly.
3:1
\(\mathsf{ \frac{3}{1} }\)
three inches to one foot
Suppose an architect is creating plans for a building and wants a room to have a length of ten feet. She is using a scale of three inches to one foot. How long should the blueprint version of room be?
These are the steps you could follow to answer this question.
| Set up a proportion. | If x equals the length of the drawn room in inches, then \(\small\mathsf{ \frac{3}{1} = \frac{x}{10} }\). |
| Cross multiply. | 30 = x |
| Answer the problem. | The length of the room on the blueprint should be 30 inches. |
Now see if you can solve a similar problem. Suppose you are drawing up plans for a new multi-level building, and you know that each floor should be about ten feet tall. You want the building to have five floors. How many inches will you need to draw the side of the building if you are using a scale of two inches to one foot? Work out the problem in your notebook. Then click on the Answer Button below to check your work.
| Your first step is to figure out the total height of the building. | If each floor is ten feet tall and there are five floors, the building will be fifty feet tall. |
| Next, set up a proportion to solve for inches. | Let x equal the length in inches. \(\small\mathsf{ \frac{2}{1} = \frac{x}{50} }\) |
| Cross multiply and solve. | 100 = x Your drawing will be 100 inches. |
