AnswersSRC 2022 MJ Grade 8 Pre-Algebra Q1Dilations

Finding the Hypotenuse in Right Triangles Answers

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1
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Which equation could be used to find the length of the hypotenuse?

Question illustration
A
2 squared + 5 squared = c squared
Option A
B
2 squared + c squared = 5 squared
Option B
C
c squared minus 2 squared = 5 squared
Option C
D
5 squared minus 2 squared = c squared
Option D
2
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Lewis needed to find the difference in lengths between the hypotenuse and the longest leg of this triangle. His work is shown below.What errors did Lewis make? Check all that apply.

Question illustration
A
He simplified incorrectly. It should be 20 instead of 200.
Option A
B
He found the difference between the hypotenuse and the short leg instead of the long leg.
C
He evaluated incorrectly. It should be .
Option C
D
He evaluated incorrectly. It should be .
Option D
E
He should not have taken the square root of each side to get rid of the exponent.
3

Samantha and Mia each left Julia’s house at the same time. Mia walked north at 7 kilometers per hour. Samantha ran west at 11 kilometers per hour. How far apart were they after one hour? Round the answer to the nearest tenth.

Question illustration
A
7.7 km
B
8.4 km
C
13.0 km
D
18.0 km
4

What is the length of the hypotenuse of the triangle?

Question illustration
A
cm
Option A
B
cm
Option B
C
cm
Option C
D
cm
Option D
5

Sanjay, Colby, and Arpitha are training to run a marathon. On Saturday, Sanjay ran miles, Colby ran 13 miles, and Arpitha ran the shortest route from the library to her house, as shown in the diagram. Which list shows the names in order from the person who ran the shortest distance to the one who ran the greatest distance?

Question illustration
A
Colby, Sanjay, Arpitha
B
Sanjay, Arpitha, Colby
C
Sanjay, Colby, Arpitha
D
Arpitha, Sanjay, Colby
6

Mrs. Ibarra wants to create a right triangle for a geometry test. She plans to use 15, 36, and 41 as side lengths.Select the four true statements regarding the side lengths Mrs. Ibarra chose.

A
, so the side lengths will form a triangle.
Option A
B
, so those lengths will not form a triangle.
Option B
C
15 squared + 36 squared = 1,521
Option C
D
41 squared = 1,681
Option D
E
Since , it will not be a right triangle.
Option E
F
15 squared + 36 squared = 297
Option F
G
41 squared = 82
Option G
7

Frankie wants to build a path from one corner of his yard to the opposite corner. His yard measures 20 ft. x 32 ft. What will be the length of his path to the nearest tenth of a foot?

A
21.5 ft
B
25.0 ft
C
32.6 ft
D
37.7 ft
8

Reynaldo rode his bike 2 miles north and 3 miles east. Which equation should he use to find the distance, d, that takes him directly back home?

Question illustration
A
2 squared + 3 squared = d squared
Option A
B
3 squared minus 2 squared = d squared
Option B
C
d squared + 2 squared = 3 squared
Option C
D
d squared + 3 squared = 2 squared
Option D
9

Which equation could be used to find the length of the hypotenuse?

Question illustration
A
5 squared + 8 squared = c squared
Option A
B
5 squared + c squared = 8 squared
Option B
C
c squared minus 5 squared = 8 squared
Option C
D
8 squared minus 5 squared = c squared
Option D
10

What is the length of the hypotenuse of the triangle?

Question illustration
A
26 ft
B
34 ft
C
68 ft
D
74 ft

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