Special Right Triangles Answers

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6

Arielle is building the wooden framework for the roof of a house. She needs the angle created by the vertical and horizontal boards of the frame to be a right angle. The height of the vertical board is 12 feet. The length of the horizontal board is 15 feet. The support beam that will connect the ends of the two boards measures 20 feet.

A
It is an acute triangle. About 0.8 foot needs to be removed from the 20-foot board to create a right triangle.
B
It is an obtuse triangle. About 0.8 foot needs to be removed from the 20-foot board to create a right triangle.
C
It is an acute triangle. About 7 feet need to be removed from the 20-foot board to create a right triangle.
D
It is an obtuse triangle. About 7 feet need to be removed from the 20-foot board to create a right triangle.
10

Which best explains whether a triangle with side lengths 5 cm, 13 cm, and 12 cm is a right triangle?

A
The triangle is a right triangle because 52 + 122 = 132.
B
The triangle is a right triangle because 5 + 13 > 12.
C
The triangle is not a right triangle because 52 + 132 > 122.
D
The triangle is not a right triangle because 5 + 12 > 13.
11

A right triangle has side lengths 4 units, 5 units, and x units. It is unknown if the missing length is the longest or shortest side.Rounded to the nearest tenth, what is the difference between the possible values of x?

A
3.0 units
B
3.4 units
C
6.4 units
D
8.0 units
12

Two sides of an acute triangle measure 5 inches and 8 inches. The length of the longest side is unknown.What is the greatest possible whole-number length of the unknown side?

A
8 inches
B
9 inches
C
12 inches
D
13 inches
13

Which set of numbers can represent the side lengths, in inches, of an acute triangle?

A
4, 5, 7
B
5, 7, 8
C
6, 7, 10
D
7, 9, 12
14

The longest side of an acute isosceles triangle is 8 centimeters. Rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?

A
4.0 cm
B
4.1 cm
C
5.6 cm
D
5.7 cm
15

Which best explains whether a triangle with side lengths 2 in., 5 in., and 4 in. is an acute triangle?

A
The triangle is acute because 22 + 52 > 42.
B
The triangle is acute because 2 + 4 > 5.
C
The triangle is not acute because 22 + 42 < 52.
D
The triangle is not acute because 22 < 42 + 52.
16

The longest side of an acute isosceles triangle is 12 centimeters. Rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?

A
6.0 cm
B
6.1 cm
C
8.4 cm
D
8.5 cm
17

An acute triangle has two sides measuring 8 cm and 10 cm. What is the best representation of the possible range of values for the third side, s?

A
2 < s < 18
B
6 < s < 12.8
C
s 18
D
s 12.8
18

The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown.What is the smallest possible perimeter of the triangle, rounded to the nearest tenth?

A
41.0 in.
B
51.2 in.
C
72.4 in.
D
81.2 in.
19

Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?

A
acute, because 62 + 102 < 122
B
acute, because 6 + 10 > 12
C
obtuse, because 62 + 102 < 122
D
obtuse, because 6 + 10 > 12
20

Which set of numbers can represent the side lengths, in centimeters, of a right triangle?

A
8, 12, 15
B
10, 24, 26
C
12, 20, 25
D
15, 18, 20

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