1. Which set represents a Pythagorean triple? (1 point)
27, 38, 42
33, 44, 55
35, 38, 42
68, 72, 81
2. Which number completes the Pythagorean triple: 12, 16, ____? (1 point)
18
20
22
24
3. Which set represents a Pythagorean triple? (1 point)
1, 2, 4
2, 4, 6
3, 4, 10
5, 12, 13
4. A television set is 36 inches wide and has a diagonal length of 42 inches. To the nearest inch, how tall is the set? (1 point)
9
13
22
55
My answers:
1. 33,44,55
2. 20
3. 127
4. 1.9
5. 22
#3,
5,12,13 is a Pythagorean triple
since 5^2 + 12^2 = 13^2
I don't understand your answer of 127.
the rest are correct
Oh sorry Reiny, I was thinking of something else and accidentally typed 127 XDD my bad. And I already handed it in- thanks though:)
1. The set that represents a Pythagorean triple is 33, 44, 55.
2. The number that completes the Pythagorean triple is 20.
3. The set that represents a Pythagorean triple is 5, 12, 13.
4. To find the height of the television set, we can use the Pythagorean theorem. The width and diagonal length of the set form a right triangle. Let the height be h. Using the theorem, we have 36^2 + h^2 = 42^2. Solving for h, we get h = 22.
Note: It seems like there is a mistake in your numbering because there is no question 5 mentioned.
1. To determine if a set represents a Pythagorean triple, we need to apply the Pythagorean theorem. The theorem states that in any right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. So, to check each set:
- 27, 38, 42: To determine if these numbers form a Pythagorean triple, we can check if 27^2 + 38^2 equals 42^2.
- 33, 44, 55: To determine if these numbers form a Pythagorean triple, we can check if 33^2 + 44^2 equals 55^2.
- 35, 38, 42: To determine if these numbers form a Pythagorean triple, we can check if 35^2 + 38^2 equals 42^2.
- 68, 72, 81: To determine if these numbers form a Pythagorean triple, we can check if 68^2 + 72^2 equals 81^2.
Based on these calculations, we can see that the second set, 33, 44, 55, satisfies the Pythagorean theorem. Therefore, the correct answer is 33, 44, 55.
2. To find the missing number in a Pythagorean triple, we need to determine the relationship between the two known numbers. In a Pythagorean triple, the square of one side is equal to the sum of the squares of the other two sides.
Given the Pythagorean triple 12, 16, ____, we need to find the missing number. To do this, we can use the Pythagorean theorem:
12^2 + 16^2 = __^2
144 + 256 = __^2
400 = __^2
Taking the square root of both sides, we find that the missing number is 20. Therefore, the correct answer is 20.
3. Similar to the first question, we need to apply the Pythagorean theorem to determine if a set represents a Pythagorean triple. Checking each set:
- 1, 2, 4: To determine if these numbers form a Pythagorean triple, we can check if 1^2 + 2^2 equals 4^2.
- 2, 4, 6: To determine if these numbers form a Pythagorean triple, we can check if 2^2 + 4^2 equals 6^2.
- 3, 4, 10: To determine if these numbers form a Pythagorean triple, we can check if 3^2 + 4^2 equals 10^2.
- 5, 12, 13: To determine if these numbers form a Pythagorean triple, we can check if 5^2 + 12^2 equals 13^2.
Based on these calculations, we can see that the last set, 5, 12, 13, satisfies the Pythagorean theorem. Therefore, the correct answer is 5, 12, 13.
4. To find the height of the television set, we can use the Pythagorean theorem. Given that the width is 36 inches and the diagonal length is 42 inches, we can consider the width (36 inches) as one side of a right triangle, the height as the other side, and the diagonal length (42 inches) as the hypotenuse.
Applying the Pythagorean theorem, we have:
36^2 + height^2 = 42^2
1296 + height^2 = 1764
height^2 = 1764 - 1296
height^2 = 468
Taking the square root of both sides, we find that the height is approximately 21.63 inches. Since we need the answer to the nearest inch, the nearest whole number is 22 inches. Therefore, the correct answer is 22 inches.