Lesson 7.1: Scale Drawings
Objectives
1) Expected that students will calculate dimensions on a scale drawing usig a scale factor.

Architects and map-makers are examples of people who use scale drawings in their field. It's basically about building models of the real thing on a suitable scale.

Scale
Drawings		 A scale drawing is a drawing that represents a real object. The scale of the drawing is the ratio of the size of the drawing to the actual size of the object. Common Scale Drawings include blueprints and maps.
Scale
Factor		 The scale factor is the ratio of the new size to the corresponding old size. For example, if a model car has a scale factor of 1:10 or 1/10 or 0.1, then a part that is one centimeter on the model would correspond to 10 cm on the real car.


On a blueprint, a hallway is measured to be 3.5 cm long. The scale factor of the drawing is 1:100. What is the length of the hallway going to be?

 


Solution:
We can set up a ratio that shows the relationship between the blueprint and the real thing.

Note that we kept the smaller numbers (the numbers corresponding to the blueprint) on the top and the larger numbers (corresponding to the "real thing") on the bottom. It doesn't matter whether we have the smaller on the top or bottom - just as long as they are both on top or bottom.

Next, we solve for x. We can do this by cross-multiplying (1 time x and 100 times 3.5).
We find that x = 350 cm. And not that this is equivalent to x = 3.5 meters. The hallway is to be, therefore, 3.5 meters long.

Scale Drawing Examples

Example 1: ~Solve the question in you notebook then check your solution.~

A map with a scale of 1:500 000 has a lake that is shown as 2.5 cm long. How long is the actual lake?



Example 2: ~Solve the question in you notebook then check your solution.~

A patio will be 12 ft wide. If a blueprint where 0.5 in. represents 5 ft., then how wide must the deck be shown on the blueprint?




Practice Work

Read pages 358-362 in your .
Do Exercises 1-9 on pages 363-365.
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