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Triangles and Their Side Lengths Answers

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Steven is cutting an 11 ft piece of lumber into three pieces to build a triangular garden. Which diagram shows a way in which he can cut the wood to create three pieces that can form a triangle?

A
A piece of wood is cut into 3 pieces. The pieces are: 2 feet, 2 feet, and 7 feet.
Option A
B
A piece of wood is cut into 3 pieces. The pieces are: 1 foot, 4 feet, 6 feet.
Option B
C
A piece of wood is cut into 3 pieces. The pieces are: 3 feet, 2 feet, and 6 feet.
Option C
D
A piece of wood is cut into 3 pieces. The pieces are: 3 feet, 4 feet, 4 feet.
Option D
2
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Triangle A B C is shown. Side A B has a length of 12. Side B C has a length of x. Side A C has a length of 15.

Question illustration
A
0
B
1
C
3
D
7
3

A triangle has side lengths measuring 3x cm, 7x cm, and h cm. Which expression describes the possible values of h, in cm?

A
4x < h < 10x
B
10x < h < 4x
C
h = 4x
D
h = 10x
4

Triangle QRS has the angle measures shown.

Question illustration
1
18
5
54
1
108
2
216
5

must

l
less than 90°.
g
greater than 90°.
c
congruent to angle B.
c
congruent to angle C.
6

If triangle DEF has a 90° angle at vertex E, which statements are true? Select two options.

A
Triangle DEF is an obtuse triangle.
B
The angle at vertex D is acute.
C
The angle at vertex F is obtuse.
D
Triangle DEF is a right triangle.
E
The angle at vertex D is obtuse.
7

In triangle XYZ, m∠Z > m∠X + m∠Y. Which must be true about △XYZ?

A
m∠X + m∠Z < 90°
B
m∠Y > 90°
C
∠X and∠Y are complementary
D
m∠X + m∠Y < 90°
8

3 connecting lines are shown. Line D F is horizontal. Line D E is about half the length of line D F. Line F E is about one-third of the length of line D F.

Question illustration
E
EF + FD > DE
E
ED + EF < DF
E
ED + EF > DF
E
EF + FD < DE
9

Which statements about the diagram are true? Select three options.

A
D E + E F greater-than D F
Option A
B
is an isosceles triangle.
Option B
C
5 less-than D F less-than 13
Option C
D
D E + D F less-than E F
Option D
E
is a scalene triangle.
Option E
10

Which are the possible side lengths of a triangle?

A
3 cm, 5 cm, 9 cm
B
4 cm, 8 cm, 10 cm
C
6 cm, 9 cm, 17 cm
D
8 cm, 10 cm, 18 cm

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