AnswersOH-Geometry BArea and Perimeter of Triangles

Area and Perimeter of Triangles — Unit test Answers

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1
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Law of sines:

Question illustration
A
only 90°
B
only 155°
C
20° and 110°
D
45° and 135°
2
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The law of cosines for RST can be set up as 52 = 72 + 32 – 2(7)(3)cos(S). What could be true about RST?Law of cosines: a2 = b2 + c2 – 2bccos(A)

Question illustration
A
r = 5 and t = 7
B
r = 3 and t = 3
C
s = 7 and t = 5
D
s = 5 and t = 3
3

Law of cosines: a2 = b2 + c2 – 2bccos(A)

Question illustration
A
92 = y2 + 192 – 2(y)(19)cos(41°)
B
y2 = 92 + 192 – 2(y)(19)cos(41°)
C
92 = y2 + 192 – 2(9)(19)cos(41°)
D
y2 = 92 + 192 – 2(9)(19)cos(41°)
4

A kite is made up of two isosceles triangles, KIT and KET, with the lengths shown. The top triangle of the kite, ΔKIT, is made from approximately 17 square inches of material.Heron’s formula: Area =

Question illustration
A
31 square inches
B
34 square inches
C
48 square inches
D
62 square inches
5

Triangle ABC is a sketch of a triangular flower bed that has an area of 65.1 square feet.Trigonometric area formula: Area =

Question illustration
A
17 feet
B
33 feet
C
40 feet
D
50 feet
6

In right triangle XYZ, the right angle is located at vertex Y. The length of line segment XY is 12.4 cm. The length of line segment YZ is 15.1 cm.

A
34.8°
B
39.4°
C
50.6°
D
55.2°
7

Which equation can be used to find the length of ?

Question illustration
A
(10)sin(40o) = AC
B
(10)cos(40o) = AC
C
= AC
Option C
D
= AC
Option D
8

The diagonal of rectangle ABCD measures 2 inches in length.

Question illustration
A
1 inch
B
inches
Option B
C
4 inches
D
inches
Option D
9

Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse A B is 26, the length of A C is 10, and the length of B C is 24.

Question illustration
A
Five-thirteenths
Option A
B
Twelve-thirteenths
Option B
C
Twelve-fifths
Option C
D
Thirteen-twelfths
Option D
10

An acute triangle has side lengths 21 cm, x cm, and 2x cm. If 21 is one of the shorter sides of the triangle, what is the greatest possible length of the longest side, rounded to the nearest tenth?

A
18.8 cm
B
24.2 cm
C
42.0 cm
D
72.7 cm
11

A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm.What is the approximate area of the triangle? Round to the nearest tenth.Area of a triangle = bh

Question illustration
A
68.7 cm2
B
161.8 cm2
C
381.3 cm2
D
450.0 cm2
12

The lengths of two sides of a right triangle are 5 inches and 8 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth.

A
2.4 inches
B
3.2 inches
C
10.0 inches
D
15.7 inches
13

Which statements are true about triangle QRS? Select three options.

A
The side opposite ∠Q is RS.
B
The side opposite ∠R is RQ.
C
The hypotenuse is QR.
D
The side adjacent to ∠R is SQ.
E
The side adjacent to ∠Q is QS.
14

Law of sines:

Question illustration
A
15°
B
30°
C
45°
D
60°
15

Triangle V U W is shown. The length of side W V is 6 centimeters, the length of side W U is 3 StartRoot 3 EndRoot centimeters, and the length of side U V is 3 centimeters.

Question illustration
A
m∠V = 30°, m∠U = 60°, m∠W = 90°
B
m∠V = 90°, m∠U = 60°, m∠W = 30°
C
m∠V = 30°, m∠U = 90°, m∠W = 60°
D
m∠V = 60°, m∠U = 90°, m∠W = 30°
16

Triangle L J K is shown. Angle J L K is a right angle. The length of the hypotenuse is 15 inches and the length of the side adjacent to the right angle is 10 inches. The angle between the 2 sides is x.

Question illustration
A
sin(x) =
Option A
B
sin(x) =
Option B
C
cos(x) =
Option C
D
cos(x) =
Option D
17

Trigonometric area formula: Area =

Question illustration
A
70.5 square units
B
111.3 square units
C
185.4 square units
D
222.5 square units
18

The hypotenuse of a 45°-45°-90° triangle measures units.

Question illustration
A
11 units
B
units
Option B
C
22 units
D
units
Option D
19

The equation can be used to find the length of .

Question illustration
A
19.3 in.
B
21.3 in.
C
23.5 in.
D
68.0 in.
20

Law of cosines: a2 = b2 + c2 – 2bccos(A)

Question illustration
A
34°
B
41°
C
51°
D
56°

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