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State if the three sides lengths form a right triangle. 10) 9, 7, √125 11) √65, 4, 9 12) 12, 2√26, 15 13)...

State if the three sides lengths form a right triangle.
10) 9, 7, √125
11) √65, 4, 9
12) 12, 2√26, 15
13) 5√3, 5, 10

Answer

  1. To determine if the sides form a right triangle, use the Pythagorean theorem: a² + b² = c², where c is the hypotenuse.

    For 9, 7, √125:

    9² + 7² = 81 + 49 = 130

    (√125)² = 125

    Since 130 ≠ 125, these sides do not form a right triangle.

  2. For √65, 4, 9:

    (√65)² + 4² = 65 + 16 = 81

    9² = 81

    Since 81 = 81, these sides form a right triangle.

  3. For 12, 2√26, 15:

    12² + (2√26)² = 144 + 4*26 = 144 + 104 = 248

    15² = 225

    Since 248 ≠ 225, these sides do not form a right triangle.

  4. For 5√3, 5, 10:

    (5√3)² + 5² = 75 + 25 = 100

    10² = 100

    Since 100 = 100, these sides form a right triangle.

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