Testinar Grade 8 math

The Pythagorean Theorem

Learn to reason about and solve Grade 8 problems involving The Pythagorean Theorem.

CH05-06 Geometry and Measurement
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. Two points on a coordinate plane are located at \((0, 0)\) and \((3, 4)\). What is the distance between these two points?

    The Pythagorean Theorem visual for G8-C05-T06-Q012
    1. \(5\)
    2. \(7\)
    3. \(12\)
    4. \(25\)

  2. A right triangle has legs of length \(6\) and \(8\). What is the length of the hypotenuse?

    1. \(10\)
    2. \(12\)
    3. \(11\)
    4. \(14\)

  3. A right triangle has legs of \(5\) and \(12\). What is the hypotenuse?

    1. \(7\)
    2. \(13\)
    3. \(17\)
    4. \(15\)

  4. In a right triangle, one leg is \(8\) cm and the hypotenuse is \(17\) cm. Find the other leg.

    1. \(9\) cm
    2. \(15\) cm
    3. \(19\) cm
    4. \(25\) cm

  5. A right triangle has legs of \(3\) and \(4\). Which statement is true?

    1. The hypotenuse is \(7\)
    2. The hypotenuse is \(5\)
    3. The legs are \(3\) and \(5\)
    4. The hypotenuse is \(1\)

  6. A ladder leaning against a wall forms a right triangle. The ladder is \(13\) feet long (hypotenuse), and the base is \(5\) feet from the wall. How high up the wall does it reach?

    1. \(8\) feet
    2. \(12\) feet
    3. \(18\) feet
    4. \(65\) feet

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

    1. \(7, 10, 12\)
    2. \(6, 8, 10\)
    3. \(4, 5, 10\)
    4. \(1, 2, 4\)

  8. A right triangle has legs of \(7\) and \(24\). What is the hypotenuse?

    1. \(17\)
    2. \(20\)
    3. \(25\)
    4. \(31\)
Teacher and parent reference

Answer key and explanations

  1. A. \(5\)

    The distance formula uses the Pythagorean Theorem: \(d=\sqrt{(3-0)^2+(4-0)^2}=\sqrt{9+16}=\sqrt{25}=5\) (the 3-4-5 triple).

  2. A. \(10\)

    Pythagorean Theorem: \(a^2+b^2=c^2\), so \(6^2+8^2=c^2\), \(36+64=100\), \(c=\sqrt{100}=10\).

  3. B. \(13\)

    Using the Pythagorean Theorem: \(5^2+12^2=c^2\) gives \(25+144=169\), so \(c=13\) (the 5-12-13 triple).

  4. B. \(15\) cm

    Rearranging \(a^2+b^2=c^2\): \(8^2+b^2=17^2\) gives \(64+b^2=289\), so \(b^2=225\) and \(b=15\) (the 8-15-17 triple).

  5. B. The hypotenuse is \(5\)

    The 3-4-5 Pythagorean triple is among the most common. \(3^2+4^2=9+16=25\), so \(c=5\).

  6. B. \(12\) feet

    The 5-12-13 triple applies: \(5^2+h^2=13^2\) gives \(25+h^2=169\), so \(h=12\) feet.

  7. B. \(6, 8, 10\)

    Check: \(6^2+8^2=36+64=100=10^2\). This is a scaled 3-4-5 triple (all multiplied by 2).

  8. C. \(25\)

    Using the Pythagorean Theorem: \(7^2+24^2=49+576=625\), so \(c=25\) (the 7-24-25 triple).

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