Page 240 - Algebra 1

A scale drawing is a drawing that reduces or enlarges the dimensions of an object by a constant factor. Maps and blueprints are examples of scale drawings. The scale is a ratio showing the relationship between a scale drawing or model and the actual object.
Application: Scale Drawings
A desk is designed to have three drawers on the right side. In the scaled design drawing, the width of the drawers is 4 centimeters. If the scale of the drawing is 1 cm:7 cm, how wide will the actual desk drawers be?
Math Reasoning
Generalize Will the proportions _x = _5 and
_4 _6 4 6
x = 5 give the same
values for x? Explain your reasoning.
Example
3
SOLUTION Set up a proportion to solve the problem.
drawing length = __
_1 _4
= x
actual length 7 1·x=4·7
x = 28
The width of the actual desk drawers will be 28 centimeters.
Scale factors of side lengths can also be used to determine the ratios of perimeters, areas, and volumes of figures and solids.
Exploration Changing Dimensions Students may work in groups of two or three.
a. Begin with 1 cube and let the length of an edge equal 1 unit. Then the perimeter of the base of the cube is 4 · 1 = 4 units, the area of the base of thecubeis1·1=1squareunit,andthevolumeof thecubeis
1 · 1 · 1 = 1 cubic unit. Copy and complete the table below.
Materials
• 64 cubes per pair or group
Alternate Materials (blocks, cheese or sugar cubes are possible examples)
Length of Edge (units)
Perimeter of the Base (units)
Area of the Base (square units)
Volume of the Base (cubic units)
1
2
3
b. Use the cubes to build another cube with edge lengths of 2 units. Record your answers in the table.
c. Repeat for a cube with a side length of 3 units. Record your answers in the table.
Use the rows with edge lengths of 2 and 3 from the table.
d. What is the scale factor of the edge lengths?
e. Find the ratio of the perimeters. How does this ratio compare to the scale factor?
f. Find the ratio of the areas. How does this ratio compare to the scale factor?
Lesson 36 225