Objects at Scale
Scale drawings allow architects, engineers, and mapmakers to represent large objects on a smaller paper drawing. To be successful at solving problems involving scale drawings, you need to grasp the concept of scale and learn to calculate the scale factor.
Scale refers to the relationship between a measurement on the drawing and the actual size of the object. For example, on a blueprint, the scale might indicate that 1 cm on the paper equals 10 feet in real life. This allows you to depict something enormous on a small drawing.
The scale factor is essentially a ratio that compares the size on the drawing to the actual size. It serves as a guide to help convert between the two. You can use the following formula:
Actual Size = (Size on Drawing) x (Scale Factor)
Let's look at an example. Say you're building an awesome new treehouse, and you have some plans drawn up by an architect. These plans use a scale of 1/4 inch on the drawing equals 1 foot in real life. This is the scale that is provided.
Now on these plans, you measure the ladder that leads up to the treehouse entrance, and it is 2 inches long on the drawing. This is the size on the drawing that you need to convert to actual size.
To do this, you first need to determine the scale factor, which is the opposite of the scale. The scale here is 1/4 inch = 1 foot. So the scale factor is 1 foot per 1/4 inch, or 4 feet per 1 inch. With the scale factor figured out, you can plug the information into the formula:
Actual Size = (Size on Drawing) x (Scale Factor)
The size on the drawing is 2 inches. The scale factor is 4 feet per 1 inch. Plugging this in:
Actual Size = (2 inches/1) x (4 feet / 1 inch)
There are inches in the numerator of the first term and the denominator, so these cancel out and leave feet as the only unit. Multiplying it out:
Actual Size = 2 x 4 feet
Which gives you the final answer:
Actual Size = 8 feet
To excel at solving scale drawing problems, start by identifying the scale used on the drawing, which shows the relationship to the real object. Next, locate the measurement on the scaled drawing that you want to convert, like the width of a bridge on a map. Then, figure out the scale factor, which is the opposite of the scale. For example, if the scale is 1 cm = 10 feet, the scale factor is 10 feet per cm. Now you can apply the formula to calculate the actual size. Finally, double check that your units match up properly.