Pythagoras Practice Unit Test

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| By Mrsmosher
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Pythagoras Practice Unit Test - Quiz

Questions and Answers
  • 1. 

    Question No Image

    • A.

      10-11

    • B.

      11-12

    • C.

      12-13

    • D.

      13-14

    Correct Answer
    C. 12-13
    Explanation
    The given answer, 12-13, represents the range of values between 12 and 13. The pattern in the question suggests that each pair of numbers represents a range or interval. Therefore, the answer 12-13 indicates that the numbers in the range can be any value between 12 and 13, including both 12 and 13 themselves.

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  • 2. 

    Question No Image

    • A.

      1-2

    • B.

      2-3

    • C.

      3-4

    • D.

      4-5

    Correct Answer
    D. 4-5
  • 3. 

    Use the Pythagorean Theorem to find the value of the hypotenuse.a=3b=4c-?

    • A.

      10

    • B.

      12

    • C.

      5

    • D.

      6

    • E.

      4

    Correct Answer
    C. 5
    Explanation
    Using the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, we can solve for the value of the hypotenuse. Given that side a is 3 and side b is 4, we can square both sides and add them together: 3^2 + 4^2 = 9 + 16 = 25. Taking the square root of 25 gives us 5, which is the length of the hypotenuse. Therefore, the correct answer is 5.

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  • 4. 

    Using the Pythagorean Theorem, find the value of a.a=?b=6c=10

    • A.

      8

    • B.

      12

    • C.

      3

    • D.

      1

    • E.

      9

    Correct Answer
    A. 8
    Explanation
    By using the Pythagorean Theorem, we can find the value of a. The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, a is unknown, b is given as 6, and c is given as 10. We can substitute these values into the equation and solve for a. Therefore, the value of a is 8.

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  • 5. 

    A 26 foot ladder leans against a house and reaches a window that is 24 feet high. How far from the base of the house is the bottom of the ladder?

    • A.

      5 feet

    • B.

      35 feet

    • C.

      10 feet

    • D.

      15 feet

    • E.

      14 feet

    Correct Answer
    C. 10 feet
    Explanation
    The ladder forms a right triangle with the house and the ground. The height of the window is the length of one side of the triangle, and the length of the ladder is the hypotenuse. We can use the Pythagorean theorem to find the length of the other side of the triangle. Let's call this side "x". According to the theorem, x^2 + 24^2 = 26^2. Simplifying this equation gives us x^2 + 576 = 676. Subtracting 576 from both sides gives us x^2 = 100. Taking the square root of both sides gives us x = 10. Therefore, the bottom of the ladder is 10 feet away from the base of the house.

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  • 6. 

    Savannah told Paul that she knew which of the three numbers 6, 8, or 10 was the length of the hypotenuse of the right triangle. What is the length of the hypotenuse?

    • A.

      6, because the hypotenuse is always the shortest side.

    • B.

      8, because the hypotenuse is in between the two legs of the triangle.

    • C.

      10, because 10 is the largest number and the hypotenuse is always the longest side of the triangle.

    • D.

      There is not enough information to determine the length of the hypotenuse.

    Correct Answer
    C. 10, because 10 is the largest number and the hypotenuse is always the longest side of the triangle.
    Explanation
    The correct answer is 10 because the hypotenuse is always the longest side of the triangle. In a right triangle, the hypotenuse is opposite the right angle and is always the side opposite the longest side. Since 10 is the largest number given, it is the length of the hypotenuse.

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  • 7. 

    Breanna has a TV that has a 37 inch diagonal screen. The width of the TV is 12 inches. What is the length of the TV?

    • A.

      35 inches

    • B.

      38 inches

    • C.

      49 inches

    Correct Answer
    A. 35 inches
    Explanation
    Since the TV has a diagonal screen of 37 inches and a width of 12 inches, we can use the Pythagorean theorem to find the length. The Pythagorean theorem states that the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides (width and length). In this case, we can set up the equation as 37^2 = 12^2 + length^2. Solving for length, we find that the length of the TV is 35 inches.

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  • 8. 

    How far up a wall will an ladder reach that measures 11 meters, if the foot of the ladder must be 4 meters from the base of the wall?

    • A.

      5.5 meters

    • B.

      8 meters

    • C.

      11.7 meters

    • D.

      10.2 meters

    Correct Answer
    D. 10.2 meters
    Explanation
    The ladder forms a right triangle with the wall and the ground. The length of the ladder is the hypotenuse of the triangle, and the distance from the foot of the ladder to the base of the wall is one of the legs. Using the Pythagorean theorem (a^2 + b^2 = c^2), we can calculate the length of the other leg, which represents how far up the wall the ladder reaches. In this case, the length of the ladder is 11 meters and the distance from the foot of the ladder to the base of the wall is 4 meters. By substituting these values into the Pythagorean theorem, we can solve for the length of the other leg, which is approximately 10.2 meters.

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  • 9. 

    Ms. Coney made a triangle. She said that the hypotenuse is 13 inches and one of the legs is 5 inches. What is the length of the other leg?

    • A.

      72 inches

    • B.

      13.9 inches

    • C.

      12 inches

    Correct Answer
    C. 12 inches
    Explanation
    In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This relationship is known as the Pythagorean theorem. In this case, the hypotenuse is given as 13 inches and one of the legs is given as 5 inches. Using the Pythagorean theorem, we can calculate the length of the other leg by subtracting the square of the known leg from the square of the hypotenuse, and then taking the square root of the result. In this case, it would be √(13^2 - 5^2) = √(169 - 25) = √144 = 12 inches.

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  • 10. 

    To get from point A to point B Myranda must avoid walking through the pond. She walks 34 meters south and 41 meters east. How many meters is the shortest distance from point A to point B?

    • A.

      53.3 meters

    • B.

      22.9 meters

    • C.

      75 meters

    Correct Answer
    A. 53.3 meters
    Explanation
    The shortest distance from point A to point B can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the distance south and the distance east form the two sides of a right triangle. Using the Pythagorean theorem, we can calculate the length of the hypotenuse, which represents the shortest distance from point A to point B. The square of the distance south (34 meters) is 1156, and the square of the distance east (41 meters) is 1681. Adding these two values together gives us 2837. Taking the square root of 2837 gives us approximately 53.3 meters, which is the correct answer.

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  • 11. 

    Which integer is a perfect square?

    • A.

      1

    • B.

      2

    • C.

      3

    Correct Answer
    A. 1
    Explanation
    The integer 1 is a perfect square because it can be expressed as the square of another integer, which is 1.

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  • 12. 

    Approximate the square root of 10

    • A.

      Between 4 and 5

    • B.

      Between 3 and 4

    • C.

      Between 2 and 3

    Correct Answer
    B. Between 3 and 4
    Explanation
    To approximate the square root of 10, we need to find a number between 3 and 4. This is because the square root of 9 is 3, and the square root of 16 is 4. Since 10 is closer to 9 than to 16, the square root of 10 will be between 3 and 4.

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  • 13. 

    This is a question that I found. There is only one possible answer.

    • A.

      3 units

    • B.

      4 units

    • C.

      5 units

    • D.

      16 units

    • E.

      25 units

    Correct Answer
    C. 5 units
    Explanation
    The answer is 5 units because it is the only perfect square among the given options. 5 squared is equal to 25, which is a perfect square. None of the other options can be squared to equal a whole number.

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  • 14. 

    The longest side of a right triangle is called the

    • A.

      Hypotenuse

    • B.

      Legs

    Correct Answer
    A. Hypotenuse
    Explanation
    The longest side of a right triangle is called the hypotenuse. In a right triangle, the hypotenuse is the side opposite the right angle and is always the longest side. It is named as the hypotenuse because it is connected to the two legs of the triangle, which are the other two sides that form the right angle. The hypotenuse is important in the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the two legs.

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  • 15. 

    When finding the hypotenuse, you must  ______________ the value c

    • A.

      Square

    • B.

      Square root

    • C.

      Multiply

    • D.

      Divide

    Correct Answer
    B. Square root
    Explanation
    When finding the hypotenuse, you must take the square root of the value c. This is because the hypotenuse is the longest side of a right triangle and is calculated using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. Taking the square root of c allows us to find the length of the hypotenuse.

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  • 16. 

    Which of the following is 4? Choose all answers possible.

    • A.

      Natural

    • B.

      Whole

    • C.

      Rational

    • D.

      Integer

    • E.

      Irrational

    Correct Answer(s)
    A. Natural
    B. Whole
    C. Rational
    D. Integer
    Explanation
    The number 4 is a natural number because it is a positive whole number. It is also a whole number because it is not a fraction or a decimal. Furthermore, 4 is a rational number because it can be expressed as a fraction, in this case, 4/1. Lastly, 4 is an integer because it is a whole number that can be positive, negative, or zero.

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  • 17. 

    What of the following is -91? Choose all answers possible.

    • A.

      Natural

    • B.

      Whole

    • C.

      Integer

    • D.

      Rational

    • E.

      Irrational

    Correct Answer(s)
    C. Integer
    D. Rational
    Explanation
    The number -91 is an integer because it is a whole number that can be positive or negative, without any fractional or decimal parts. It is also rational because it can be expressed as a ratio of two integers, namely -91/1.

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  • 18. 

    Which of the following is -0.75? Choose all answers possible.

    • A.

      Natural

    • B.

      Whole

    • C.

      Integer

    • D.

      Rational

    • E.

      Irrational

    Correct Answer
    D. Rational
    Explanation
    The number -0.75 is a rational number because it can be expressed as a fraction, where the numerator is a whole number (-3) and the denominator is a non-zero whole number (4). Therefore, it is rational.

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  • 19. 

    Which of the following is ? Choose all answers possible.

    • A.

      Natural

    • B.

      Whole

    • C.

      Integer

    • D.

      Rational

    • E.

      Irrational

    Correct Answer
    E. Irrational
    Explanation
    An irrational number is a number that cannot be expressed as a fraction or a ratio of two integers. It is a real number that is non-repeating and non-terminating. Examples of irrational numbers include the square root of 2 and pi. In this question, the answer is "Irrational" because it is the only option that fits the definition of a number that cannot be expressed as a fraction or a ratio of two integers.

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  • 20. 

    Which of the following is 0? Choose all answers possible.

    • A.

      Natural

    • B.

      Whole

    • C.

      Integer

    • D.

      Rational

    • E.

      Irrational

    Correct Answer(s)
    B. Whole
    C. Integer
    D. Rational
    Explanation
    The number 0 is classified as a whole number, an integer, and a rational number. A whole number includes all non-negative integers, so 0 is included. An integer includes all whole numbers and their negatives, so 0 is also included. A rational number is any number that can be expressed as a fraction, and since 0 can be written as 0/1, it is considered rational. However, 0 is not considered a natural number or an irrational number.

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  • 21. 

    Find the missing side lengths of the figure above.

    Correct Answer
    C.

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  • Current Version
  • Mar 19, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Oct 29, 2012
    Quiz Created by
    Mrsmosher
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