This document contains notes from a math lesson on computing actual lengths from a scale drawing. It includes examples of calculating scale factors from drawings and using them to determine actual lengths and widths. It also provides practice problems for students to solve. The lesson covers key concepts like determining the scale factor as a constant of proportionality between drawing and actual measurements and using it in the equation y=kx to find actual dimensions.

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Lesson 18
Aim: Computing Actual Lengths from a Scale Drawing
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Homework: Lesson 18 Problem Set #1, 4, 6, 7
QUIZ 2 Monday 10/19
Lessons 13­19
Do Now
Exit Ticket from Lesson 17

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Example 1: Basketball at Recess?
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 below. 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?
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The constant of proportionality, k = the scale factor
y = drawing length
x = actual length
In example 1: k =
y = kx

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Find the actual length: Find the actual width:

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Example 2:
The diagram shown represents a garden. The scale is 1 cm for every 20 meters of actual length. Find
the actual length and width of the garden based upon the given drawing. Each square in the drawing
measures 1 cm by 1 cm.
What is the scale factor (the constant of proportionality)?
Find actual length: Find the actual width:
k =
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y = kx

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Example 3:
A graphic designer is creating an advertisement for a tablet. She needs to englarge 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?
Find the scale factor:
Find the actual length:
Find the actual width:
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Exercise:
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 of 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, show below, from the city planning office. Use this diagram to
decide if the panels will fit through the entrance. Use a rule to measure.
a. Find the actual distance of the mall entrance and determine whether the set panels will fit.
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Step 1: Find the scale factor
Step 2: Find the actual distance of the entrance

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Closing:
• What does the scale factor tell us about the relationship between the actual picture and
the scale drawing?
• How does a scale drawing differ from other drawings?