EngageNY

Module 1

Lesson 18

COMPUTING

ACTUAL LENGTHS

FROM A SCALE

DRAWING

"Grade 7 Mathematics Module 1." Grade 7 Mathematics Module 1. 9 Sept. 2014. Web. 26 Jan. 2015. .

Example 1

Vincent proposes an idea to the Student Government to install a basketball hoop along with a court marked with all the shooting lines and boundary lines at his school for students to use at recess. He presents a plan to install a half-court design as shown. After checking with school administration, he is told it will be approved if it will fit on the empty lot that measures 25 feet by 75 feet on the school property. Will the lot be big enough for the court he planned? Explain.

Example 1 Continued

Let’s make a table:

Scale factor: 1 inch corresponds to (15 ∙ 12) inches, or

180 inches, so the scale factor is 180. Let k = 180, x

represent the scale drawing lengths in inches, and y

represent the actual court lengths in inches. The y-

values must be converted from feet to inches.

Scale Drawing Lengths:

Actual Court Lengths:

1 in.

15 ft.

2 in.

30 ft.

1 𝟐

𝟑in.

25 ft.

Example 1 Continued

To find actual length: y = 180x

y = 180(2)

y = 360 inches or 30 feet

To find actual width: y = 180x

y = 180(12

3)

y = 180

1∙5

3

y = 300 inches or 25 feet

Example 1 Continued

Solution:

The actual court measures 25 feet by 30 feet.

Will the court fit on the empty lot?

Yes, the lot will be big enough for the court Vincent

planned. The court will take up the entire width of the lot.

Example 2

The diagram shown represents a garden. The scale is 1

centimeter for every 20 meters. Each square in the

drawing measures 1 cm by 1 cm. Find the actual length

and width of the garden based upon the given drawing.

Example 2 Continued

Let’s make a table:

Using the given scale: 1 cm of scale drawing length

corresponds to 20 m of actual length; k = 20

Scale Length Width

Drawing, x

Actual, y

1 cm

20 m

8 cm

160 m

4 cm

80 m

Example 2 Continued

To find actual length: y = 20x

y = 20(8)

y = 160 m

To find actual width: y = 20x

y = 20(4)

y = 80 m

Solution: The actual length of the garden is 160 m and

the actual width of the garden is 80 m.

Example 3

A graphic designer is creating an

advertisement for a tablet. She needs to

enlarge the picture given here so that 0.25

inches on the scale picture will correspond

to 1 inch on the actual advertisement.

What will be the length and width of the

tablet on the advertisement?

Example 3 Continued

Let’s make a table:

Using an equation: Find the constant of proportionality, k: k = 4.

Equation: y = 4x where x represents the picture measurement

and y represents the actual advertisement measurement

Scale Length Width

Picture, x

Actual Advertisement, y

0.25 in.

1 in.

1 1

4in.

5 in.

1 1

8in.

4 1

2in.

Example 3 Continued

To find actual length: y = 4x

y = 4(1 1

4)

y = 5 inches

To find actual width: y = 4x

y = 4(1 1

8)

y = 4 1

2

The tablet will be 5 inches by 4 1

2inches on the actual advertisement.

Exercises

Students from the high school are going to perform one of the

acts from their upcoming musical at the atrium in the mall. The

students want to bring some of the set with them so that the

audience can get a better feel for the whole production. The

backdrop that they want to bring has panels that measure 10

feet by 10 feet. The students are not sure if they will be able to fit

these panels through the entrance of the mall since the panels

need to be transported flat (horizontal). They obtain a copy of

the mall floor plan from the city planning office.

Exercises Continued

Use this diagram to decide if the panels will fit through

the entrance. Use a ruler to measure.

Exercises Continued

Answer the following questions.

a. Find the actual distance of the mall entrance and determine

whether the set of panels will fit.

Step 1: Relationship between lengths in drawing and lengths in actual

Scale: 41

2𝑓𝑡.

1

8𝑖𝑛.

or the value of the ratio 36

1feet to inches.

Scale factor calculations: 54

1inches to inches =

541

8

= 432 (enlargement)

Exercises Continued

Step 2: Find the actual distance of the entrance

Use the given scale: 3

8∙ 36

1= 13

1

2feet wide

Will the panels fit through the mall entrance?

Yes, the set panels which are 10 feet by 10 feet will fit (lying flat)

through the mall entrance.

Exercises Continued

Answer the following questions.

b. What is the scale factor? What does it tell us?

The scale factor is 432.

Each length of the scale drawing is 1

432of the actual length.

The actual lengths are 432 times larger than the lengths of

the scale drawing.

Homework

Problem Set #1-8

Quiz corrections due tomorrow