AnswersSRC 2022 MJ Grade 8 Pre-Algebra Q1Dilations

Exploring the Pythagorean Theorem Answers

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Nadia says the hypotenuse of this right triangle has a length of 73 because the Pythagorean theorem states that .Which best describes Nadia’s solution?

Question illustration
A
She is correct because she applied the Pythagorean theorem properly and her arithmetic is accurate.
B
She is incorrect because she should have used 45 as the length of the hypotenuse.
C
She is incorrect because she should have squared each leg length and then found the sum.
D
She is correct because the hypotenuse is the longest side of the triangle.
2
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Which is a perfect square?

A
72
B
81
C
90
D
99
3

Which is a perfect square?

A
20
B
21
C
24
D
25
4

Which set of side lengths is a Pythagorean triple?

A
1, 3, 10
B
4, 5, 9
C
9, 40, 41
D
16, 30, 44
5

Which equation can be used to find x, the length of the hypotenuse of the right triangle?

Question illustration
A
16 + 63 = x
Option A
B
16 squared + 63 = x
Option B
C
(16 + 63) squared = x squared
Option C
D
16 squared + 63 squared = x squared
Option D
6

Which numbers are perfect squares? Check all that apply.

A
1
B
2
C
16
D
18
E
32
F
44
G
94
H
100
7

Ariel completed the work below to show that a triangle with side lengths of 9, 15, and 12 does not form a right triangle. Is Ariel’s answer correct?

Question illustration
A
No, Ariel should have added 122 and 152 and compared that to 92.
B
No, Ariel should have subtracted 122 from 92 and compared that to152.
C
No, Ariel should have added 92 and 122 and compared that to 152.
D
Yes, Ariel’s work is correct.
8

Which sets of side lengths represent Pythagorean triples? Check all that apply.

A
1, 2, 5
B
6, 8, 14
C
8, 15, 17
D
10, 24, 26
E
15, 20, 30
F
28, 45, 53
9

What is the length of the hypotenuse, x, if (20, 21, x) is a Pythagorean triple?

A
22
B
29
C
41
D
42
10

Imara used these steps to find the length of the hypotenuse of the right triangle.Step 1: Find the area of the square with side lengths of 20: 400 Step 2: Find the area of the square with side lengths of 15: 225Step 3: Find the sum of the areas of the two squares: 625Step 4: State the length of the hypotenuse: 625Which best describes Imara’s error?

Question illustration
A
She should have found the area of the square with side lengths of 15 first.
B
She did not correctly calculate the area of the square with side lengths of 15.
C
She should have found the sum of 15 and 20 and then squared the sum.
D
She did not find the side lengths of the square with an area of 625.

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