Pythagorean Theorem Quiz

Grade 8 · Math · Quiz

Apply the Pythagorean Theorem to find missing sides and solve real-world problems.

Questions

  1. A right triangle has legs 9 and 12. What is the hypotenuse?

    1. 13
    2. 15
    3. 17
    4. 21
    Show answer

    Answer: 15

    9²+12²=81+144=225; √225=15. This is the 3-4-5 triple scaled by 3.

  2. The set of numbers {6, 8, 10} is a Pythagorean triple.

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    Answer: True

    6²+8²=36+64=100=10². These are all Pythagorean triples in the 3-4-5 family.

  3. A right triangle has hypotenuse 13 and one leg of 5. The other leg is ___.

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    Answer: 12

    a²+5²=13² → a²=169-25=144 → a=12. The 5-12-13 triple.

  4. Which set of side lengths forms a right triangle?

    1. 2, 3, 4
    2. 4, 5, 6
    3. 9, 40, 41
    4. 7, 8, 10
    Show answer

    Answer: 9, 40, 41

    9²+40²=81+1600=1681=41². The other sets fail: e.g. 4²+5²=41≠36.

  5. A square has a diagonal of 10 cm. What is the side length? (Round to nearest tenth.)

    1. 5.0 cm
    2. 6.1 cm
    3. 7.1 cm
    4. 8.0 cm
    Show answer

    Answer: 7.1 cm

    Diagonal d=10; 2s²=100 → s²=50 → s=√50≈7.07≈7.1 cm.

  6. A right triangle with legs 1 and 1 has a hypotenuse of √2.

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    Answer: True

    1²+1²=2; √2 is the hypotenuse. This is exact — no rounding needed.

  7. Two hikers start at the same point. One walks 3 miles east, the other 4 miles north. How far apart are they?

    1. 5 miles
    2. 7 miles
    3. √7 miles
    4. 25 miles
    Show answer

    Answer: 5 miles

    3²+4²=9+16=25; √25=5. Classic 3-4-5 triangle.

  8. In the formula a² + b² = c², the variable c always represents the ___.

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    Answer: hypotenuse

    c is the hypotenuse by convention in the Pythagorean Theorem.

  9. A TV is described as 50 inches diagonally. The width is 40 inches. What is the height?

    1. 10 in
    2. 20 in
    3. 30 in
    4. 35 in
    Show answer

    Answer: 30 in

    h²+40²=50² → h²=2500-1600=900 → h=30. The 3-4-5 triple scaled by 10.

  10. The Pythagorean Theorem can be applied to any triangle, not just right triangles.

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    Answer: False

    The Pythagorean Theorem only applies to right triangles (those with a 90° angle).

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