Chapter 8.3

Problem Solving Using Proportions

Objectives

I will use proportions to solve real-life problems.

I will use similar triangles to measure objects indirectly.

Solving real-life problems

Proportions are used in architecture and manufacturing to construct scale models.

You can also use proportions to find dimensions.

Finding Dimensions

You have a scale model of a Boeing 767. The model was built using a 1 – to 250 scale. The wing span on the model is 7 ½ in. What is the wing span of an actual 767?

7.5 1250x

Finding Dimensions Continued Step 1: Set up a proportion

Step 2: Use Cross Product Property

Step 3: Solve Equation1875 = x

The wing span of a 767 is 1875 in. Convert this measurement back into feet by dividing by 12.

1875 ÷ 12 = 156 ft.

7.5 1250x

7.5 250 1x

Give it a try! The scale on a map reads 1 in = 5 mi. Find

the actual length of a road that is 2.5 in. long on the map.

Step 1: Set up a proportion

Step 2: Cross Multiply1x = 12.5 x = 12. 5 miles

52.5 1

x miin in

Finding the height of a building

To estimate the height of the Transco Tower in Huston, Texas, you measure its shadow to be about 55 m. The shadow of a 50 m flagpole is about 10 m. Estimate the height of the Transco Tower.

Height of a buildingStep 1: Set up a proportion:

Transco Tower Height = HFlagpole Height = h = 50Transco Tower Shadow = D = 55Flagpole Shadow = d = 10

Step 2: Cross Multiply and write an equationH (10) = 50 (55)

10 H = 2750Step 3: Solve the equation: H = 275

The Transco Tower is about 275 m high.

TranscoTower Height Transco Tower Shadow

Flagpole Height Flagpole shadow

5550 10H

Give it a try!

A meteorologist reports that the ratio of snowfall in January to total snowfall during the average winter is 2 to 5. If 34 inches have fallen in January of the current year, find the predicted total snowfall for the entire winter.

Proportion: 2 345 x