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Math Problems
Grade 8
Pythagorean theorem: word problems
An envelope measures
8
8
8
inches by
6
6
6
inches. A pencil is placed in the envelope at a diagonal. What is the maximum possible length of the pencil?
\newline
_
_
_
_
\_\_\_\_
____
inches
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Leah's rectangular bedroom is
12
12
12
feet by
9
9
9
feet. What is the diagonal distance from one corner to the opposite corner?
\newline
_
_
_
_
\_\_\_\_
____
feet
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Greg is building a slide for his kids. The ladder is
3
meters
3\,\text{meters}
3
meters
tall and the slide is
5
meters
5\,\text{meters}
5
meters
long. What is the distance between the ladder and the bottom of the slide?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
meters
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A flying squirrel lives in a nest that is
16
16
16
meters high in a tree. To reach a fallen acorn that is
12
12
12
meters from the base of the tree, how far will the flying squirrel have to glide?
\newline
_
_
_
_
\_\_\_\_
____
meters
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Abigail uses a table saw to cut a piece of plywood from one corner to the opposite corner. If the piece of plywood measured
16
16
16
inches by
12
12
12
inches, how long was the cut that Abigail made?
\newline
_____ inches
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Three people are sitting on a bus. Eva is seated
6
feet
6\,\text{feet}
6
feet
directly behind Mona and
8
feet
8\,\text{feet}
8
feet
directly left of Todd. How far is Mona from Todd?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
feet
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Rosanne takes a piece of plywood that is
12
12
12
inches long and uses a table saw to make a
20
20
20
-inch cut from corner to opposite corner. What was the width of the piece of plywood?
\newline
_____ inches
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Whenever she visits Newport, Ashley has to drive
12
12
12
miles due north from home. Whenever she visits Fairfax, she has to drive
16
16
16
miles due east from home. How far apart are Newport and Fairfax, measured in a straight line?
\newline
_
_
_
_
\_\_\_\_
____
miles
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Silvergrove is
15
15
15
kilometers due north of the airport, and Weston is
8
8
8
kilometers due east of the airport. How far apart are Silvergrove and Weston?
\newline
\newline
_
_
_
_
\_\_\_\_
____
kilometers
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A flying squirrel's nest is
8
meters
8\,\text{meters}
8
meters
high in a tree. From its nest, the flying squirrel glides
10
meters
10\,\text{meters}
10
meters
to reach an acorn that is on the ground. How far is the acorn from the base of the tree?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
meters
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Tyrone bicycles
12
kilometers
12\,\text{kilometers}
12
kilometers
west to get from his house to school. After school, he bicycles
16
kilometers
16\,\text{kilometers}
16
kilometers
north to his friend Colton's house. How far is Tyrone's house from Colton's house, measured in a straight line?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
kilometers
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Trudy is fishing from a small boat. Her fishing hook is
8
meters
8\,\text{meters}
8
meters
below her, and a fish is swimming at the same depth as the hook,
15
meters
15\,\text{meters}
15
meters
away. How far away is Trudy from the fish?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
meters
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Gwen bicycles
4
4
4
miles west to get from her house to school. After school, she bicycles
3
3
3
miles north to her friend Mason's house. How far is Gwen's house from Mason's house, measured in a straight line?
\newline
_
_
_
_
\_\_\_\_
____
miles
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To get from home to her friend Kyle's house, Camille would have to walk
3
3
3
miles due north. To get from home to her friend Marcy's house, Camille would have to walk
4
4
4
miles due east. What is the straight-line distance between Kyle's house and Marcy's house?
\newline
_
_
_
_
\_\_\_\_
____
miles
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Lacey is decorating a ballroom ceiling with garland. The width of the rectangular ceiling is
5
5
5
meters and the diagonal distance from one corner to the opposite corner is
13
13
13
meters. How much garland will Lacey need for the length of the ceiling?
\newline
_____ meters
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Brooke takes a sheet of paper and makes a diagonal cut from one corner to the opposite corner, making two triangles. The cut she makes is
20
20
20
centimeters long and the width of the paper is
12
12
12
centimeters. What is the paper's length?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
centimeters
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Nina is admiring a statue in Vindale Park. The statue is \(16\) feet taller than she is, and Nina is standing \(12\) feet away. How far is it from the top of the statue to Nina's head?
\newline
____feet
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An envelope measures
15
15
15
inches by
8
8
8
inches. A pencil is placed in the envelope at a diagonal. What is the maximum possible length of the pencil?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
inches
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Tara's rectangular bedroom is
4
meters
4\,\text{meters}
4
meters
by
3
meters
3\,\text{meters}
3
meters
. What is the diagonal distance from one corner to the opposite corner?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
meters
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Andy is attending a school orchestra concert. He sees his math teacher seated
16
meters
16\,\text{meters}
16
meters
ahead of him and his science teacher seated
12
meters
12\,\text{meters}
12
meters
to his right. How far apart are the two teachers?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
meters
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A flying squirrel lives in a nest that is
12
12
12
feet high in a tree. To reach a fallen acorn that is
16
16
16
feet from the base of the tree, how far will the flying squirrel have to glide?
\newline
_
_
_
_
\_\_\_\_
____
feet
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Darrell is playing hide-and-seek with Victor and Scarlett. Victor is hiding
16
meters
16\,\text{meters}
16
meters
south of Darrell, and Scarlett is hiding
12
meters
12\,\text{meters}
12
meters
east of Victor. How far apart are Darrell and Scarlett?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
meters
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From her home, Brittany would have to walk due north to get to her friend Christine's house and due east to get to her friend Tisha's house. It is
4
4
4
miles from Brittany's house to Tisha's house and a straight-line distance of
5
5
5
miles from Christine's house to Tisha's house. How far is Brittany's house from Christine's house?
\newline
_
_
_
_
_
_
_
_
_
\_\_\_\_\_\_\_\_\_
_________
miles
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Abby looks around at an assembly. She notices her younger sister to her right and her older brother
15
15
15
meters ahead of her. If Abby's brother and sister are
17
17
17
meters apart, how far apart are Abby and her younger sister?_____meters
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1
1
1
. Jane, who is
1.7
m
1.7 \mathrm{~m}
1.7
m
tall, is standing
8
m
8 \mathrm{~m}
8
m
from a
5
m
5 \mathrm{~m}
5
m
tall tree. She looks up to the top of the tree and measures the angle of elevation. What measure did she find?
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Three inches on a map represent
100
100
100
miles. The distance on the map between two cities is
7
1
2
7 \frac{1}{2}
7
2
1
inches. What is the actual distance between the cities?
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Three ballet dancers are positioned on stage. If Rita is
8
meters
8\,\text{meters}
8
meters
straight behind Ava and
6
meters
6\,\text{meters}
6
meters
directly left of Meg, how far is Ava from Meg?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
meters
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Three ballet dancers are positioned on stage. Edwin is straight behind Danielle and directly left of Katy. If Danielle and Edwin are
12
12
12
meters apart, and Katy and Danielle are
13
13
13
meters apart, what is the distance between Edwin and Katy?
\newline
_
_
_
_
\_\_\_\_
____
meters
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Adele takes a sheet of paper and cuts from one corner to the opposite corner, making two triangles. If the piece of paper is
9
9
9
inches long and
12
12
12
inches wide, how long is the diagonal cut that Adele made?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
inches
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Lakeside Street and Kingwood Avenue intersect. If Lakeside Street is
15
meters
15\,\text{meters}
15
meters
wide and Kingwood Avenue is
8
meters
8\,\text{meters}
8
meters
wide, what is the distance between two opposite corners of the intersection?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
meters
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1
1
1
. A resident lot has the shape of a parallelogram. Its base measures
20
20
20
meters. The distance between the
2
\mathbf{2}
2
parallel sides is
8
\mathbf{8}
8
meters. What is the area of the lot?
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an
80
kg
80\,\text{kg}
80
kg
non-uniform ladder that is
3.2
m
3.2\,\text{m}
3.2
m
long is placed against a frictionless wall. the center of gravity of the ladder is at a point
x
=
1.30
m
x = 1.30\,\text{m}
x
=
1.30
m
from the base of the ladder. The coefficient of static friction at the base of the ladder is
0.450
0.450
0.450
. What is the minimum angle the ladder makes with the floor for the ladder to not slip and fall.
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Danville Street and Springtown Avenue intersect. If Danville Street is
8
meters
8\,\text{meters}
8
meters
wide and Springtown Avenue is
6
meters
6\,\text{meters}
6
meters
wide, what is the distance between two opposite corners of the intersection?
\newline
_________
meters
\text{meters}
meters
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