7.5 Notes Using Proportional Relationships

Use ratios to make indirect measurements

Use scale drawings to solve problems

Indirect Measurement: any method that uses ____________________,____________________, and/or

____________________ to ____________________ an object.

Example 1: Julia would like to know how tall a nearby telephone pole is.

She notices that the pole’s shadow is 24 feet long, while her own

shadow is 7 feet long. She knows that she is 5 feet, 8 inches tall.

How tall is the telephone pole?

Example 2: Jimmy is 6 feet, 3 inches tall, and his shadow measures 9 feet long. If Jimmy’s flagpole

casts a shadow that is 30 feet, 6 inches long, how tall is the flagpole?

A scale drawing represents an object as _____________________ or ____________________ its actual size.

A scale is a _____________________ of any length in the drawing to the corresponding actual length.

Example 3: The scale for the diagram of the doghouse is 1 in : 3 ft.

Find the length of the actual doghouse.

Example 4: A rectangular fitness room is 45 feet long and 28 feet wide. Find the length

and width for a scale drawing of the room, using a scale of 1 in : 2 ft.

(hint: you will need to solve two proportions, one for the length and one for the width)

Proportional Perimeters and Areas Theorems

FLASHBACK: Perimeter of = , Area of =

Complete the following ratios using the figure to the right.

Explain the relationship between each of the ratios you just found:

Let’s summarize together: If two figures are similar and the ratio of corresponding sides (the

similarity ratio) is a

b, then

the ratio of the perimeters is , and

the ratio of the areas is .

Example 5: HJK LMN. The perimeter of HJK is 30 inches, and the area of HJK is36 square

inches. Find the perimeter and area of LMN.

Example 6: PQRS TUVW. Find the perimeter and area of TUVW.

AB BC CA

DE EF FD

perimeter of

perimeter of

ABC

DEF

area of

area of

ABC

DEF