17.3 Find Unknown Side Lengths

Name
17.3
Geometry and
Measurement—3.7.B
MATHEMATICAL PROCESSES
3.1.A, 3.1.F
Find Unknown Side Lengths
ALGEBRA
?
Essential Question
How can you find the unknown length of a side in a
polygon when you know its perimeter?
Unlock
Unlock the
the Problem
Problem
Chen has 27 feet of fencing to put around his
garden. He has already used the lengths of
fencing shown. How much fencing does he
have left for the last side?
7 ft
3 ft
4 ft
5 ft
n
Find the unknown side length.
Write an equation for the perimeter.
5 + 3 + _ + _ + n = 27
Think: If I knew the length of n, I would add
all the side lengths to find the perimeter.
5+3+
Add the lengths of the sides you know.
7
+
4 + n = 27
+ n = 27
_
Think: Addition and subtraction are
inverse operations.
n = 27 − 19
Write a related equation.
_ = 27 − 19
So, Chen has _ feet of fencing left.
Math Idea
Example
Find unknown side lengths
A symbol or letter can stand
for an unknown side length.
of a square.
The square has a perimeter of 20 inches.
What is the length of each side of the square?
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Think: A square has four sides that are equal in length.
s
s
You can multiply to find the perimeter.
s
s
• Write a multiplication equation for the perimeter.
4×
s = 20
• Use a multiplication fact you know to solve.
4 × _ = 20
So, the length of each side of the square is _ inches.
Module 17
557
5 ft
Example
Find unknown side lengths
of a rectangle.
Hint: A rectangle has
two pairs of opposite
sides that are equal
in length.
Lauren has a rectangular blanket.
The perimeter is 28 feet. The width
of the blanket is 5 feet. What is the
length of the blanket?
l
l
• Add the lengths of the sides you know.
_+_=_
• Subtract the lengths from the perimeter.
28 − _ = _
5 ft
• Divide the difference by 2.
_÷2=_
So, the length of the blanket is _ feet.
Share
Share and
and Show
Show
Find the unknown side lengths.
1. Perimeter = 25 centimeters
9 cm
9 + _ + _ + n = 25
6 cm
n
+ n = 25
3 cm
n = _ centimeters
_=_−_
2.
Perimeter = 34 meters
3.
Perimeter = 12 feet
j
7m
r
7m
r
r
r
j
j = _ meters
558
r = _ feet
Math Talk
Mathematical Processes
Explain how you can use
division to find the length
of a side of a square.
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_
Name
Unlock
Unlock the
the Problem
Problem
4.
Multi-Step Use Diagrams Latesha wants to
make a border with ribbon around a figure she
made and sketched at the right. She will use
44 centimeters of ribbon for the border. What is
the unknown side length?
A
3 centimeters
C
9 centimeters
B
13 centimeters
D
6 centimeters
3 cm
8 cm
13 cm
6 cm
5 cm
h
a.
What do you need to find? _________
b.
How will you use what you know about perimeter to help you
solve the problem? __________
c.
Write an equation to solve
the problem.
d.
Complete the sentences.
The perimeter is _ centimeters.
The sum of the sides I know is
_ centimeters.
A related subtraction equation is
_ = _ − _.
So, the length of side h is
_ centimeters.
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e.
5.
Fill in the bubble for the correct
answer choice above.
Multi-Step A rectangle has a perimeter of
34 inches. The left side is 6 inches long. What is the length
of the top side?
Module 17 • Lesson 3
559
Mathematical Processes
M
Model ¥ Reason ¥ Communicate
M
Daily
Daily Assessment
Assessment Task
Task
Fill in the bubble completely to show your answer.
6.
7.
8.
A wildlife sanctuary puts a fence around a section of
their land. The fence is 19 kilometers long. What is the
length of the unknown side?
A
5 kilometers
C
33 kilometers
B
7 kilometers
D
14 kilometers
2 km
4 km
4 km
n
4 km
Ciara buys a piece of ribbon to sew around the edges of
a square blanket. She uses 36 inches of ribbon. How long
is each side of the blanket?
A
18 inches
C
4 inches
B
9 inches
D
32 inches
Multi-Step Kenny puts a fence around his 5-sided
garden. He starts with 35 feet of fencing. After he is done,
he has 5 feet of fencing left over. How long is each side of
his garden?
A
7 feet
C
6 feet
B
5 feet
D
3 feet
g
g
g
g
g
TEXAS Test Prep
560
Eleni wants to put a fence around her square garden.
The garden has a perimeter of 28 meters. How long will
each side of the fence be?
A
8 meters
B
7 meters
C
14 meters
D
6 meters
a
a
a
a
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9.
Geometry and Measurement—3.7.B
MATHEMATICAL PROCESSES 3.1.A, 3.1.F
H o mewo rk
and Practice
17.3
Name
Find Unknown Side Lengths
ALGEBRA
Find the unknown side lengths.
1.
Perimeter = 28 centimeters
2.
Perimeter = 40 feet
11 feet
m
6 cm
6 cm
g
g
11 feet
m
m = _ centimeters
g = _ feet
Problem
Problem Solving
Solving
x
Use the diagram for 3–4.
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3.
Mitch needs to replace the fence
in his backyard. The diagram shows
the lengths of the borders of the
fence. The length of the fence is
62 meters. What is the unknown
side length? Explain how you will
solve the problem. Then write an
equation to solve the problem.
5m
12 m
7m
5m
14 m
4.
What if Mitch changes the shape of
his fence to a rectangle? How much
fencing will Mitch need? Explain.
Module 17 • Lesson 3 561
TEXAS Test Prep
Lesson
Lesson Check
Check
Fill in the bubble completely to show your answer.
Nagi has a mirror in the shape of a
hexagon. He puts a frame around it
that has a perimeter of 42 inches.
6.
How long is each side?
7.
8.
562
A
7 inches
C
8 inches
B
6 inches
D
9 inches
Zena has a square picture frame
with a perimeter of 28 inches. Which
equation can she use to find the
length of each side?
A
4 × s = 28
B
4 + s = 28
C
28 × 4 = s
D
28 + 4 = s
A farmer is putting a new fence
around a section of his ranch. The
fence is 35 kilometers long. What is
the length of the unknown side?
A
6 kilometers
B
29 kilometers
C
7 kilometers
D
35 kilometers
5 km
8 km
x
7 km
9 km
Multi-Step Glenda puts a border of
wallpaper around her bedroom wall.
The room is a rectangle with side
lengths of 3 meters and 4 meters.
If she has 20 meters of wallpaper,
how much wallpaper is left over?
9.
Multi-Step Jorge sews a trim
around the edge of a tablecloth with
8 sides. He has 32 feet of trim. If each
side of the tablecloth is 2 feet long,
how much trim will Jorge
have left?
A
13 meters
C
27 meters
A
10 feet
C
42 feet
B
6 meters
D
14 meters
B
8 feet
D
16 feet
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5.
Name
Module 17 Assessment
Vocabulary
Vocabulary
Vocabulary
Choose the best term from the box.
1.
area
The distance around a figure is the __.
perimeter
(p. 545)
Concepts
Concepts and
and Skills
Skills
Find the perimeter of the figure. Each unit is 1 centimeter.
2.
3.
_ centimeters
_ centimeters
Find the unknown side lengths.
4.
q TEKS 3.7.B
Perimeter = 33 centimeters
5.
Perimeter = 32 feet
10 cm
12 ft
4 cm
6 cm
k
g
k
12 ft
10 cm
6.
q TEKS 3.7.B
g = _ centimeters
k = _ centimeters
Use a centimeter ruler to find the perimeter.
q TEKS 3.7.B
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cm
cm
cm
cm
cm
cm
_ centimeters
Module 17
563
Fill in the bubble for the correct answer choice.
8.
9.
10.
11.
564
m
Jacob built a toolbox with a perimeter of 70 inches.
What is the length of side m? q TEKS 3.7.B
A
50 inches
B
20 inches
C
25 inches
D
10 inches
10 in.
10 in.
m
Adrienne is decorating a square picture frame. She glued
32 inches of ribbon around the edge of the frame. What
is the length of each side of the picture frame? q TEKS 3.7.B
A
4 inches
C
28 inches
B
8 inches
D
16 inches
a
a
a
a
What is the perimeter of the figure? Each unit is
1 centimeter. q TEKS 3.7.B
A
20 centimeters
C
23 centimeters
B
18 centimeters
D
9 centimeters
Jeff is making a poster for a car wash for
the Campout Club. What is the perimeter
of the poster? q TEKS 3.7.B
A
8 feet
C
6 feet
B
3 feet
D
4 feet
3 ft
1 ft
A rectangle has side lengths of 8 inches and 10 inches.
What is the perimeter of the rectangle? q TEKS 3.7.B
A
28 inches
C
32 inches
B
18 inches
D
36 inches
1 ft
3 ft
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7.
TEXAS Test Prep