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2 October, 19:04

Use the Pythagorean theorem to determine which of the following give the measures of the legs and hypotenuse of a right triangle. Which apply. 3,4,5. Or. 4,11,14. Or. 9,14,17. Or 8,14,16. Or. 8,15,17

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  1. 2 October, 19:29
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    Answer: 3, 4,5 and 17, 15,8

    give the measures of the legs and hypotenuse of a right triangle.

    Step-by-step explanation:

    In order for the measures of the legs and hypotenuse given to form a right angle triangle, they must be Pythagorean triples. A Pythagoras triple is a set of numbers that perfectly satisfy the Pythagorean theorem. The Pythagorean theorem is expressed as

    Hypotenuse² = opposite side² + adjacent side². We will apply the theorem to each set of numbers given.

    1) 3, 4, 5

    5² = 3² + 4² = 9 + 16

    25 = 25

    It is a Pythagorean triple

    2) 4, 11, 14

    14² = 11² + 4² = 121 + 16

    196 = 137

    It is a Pythagorean triple

    3) 9, 14, 17

    17² = 14² + 9² = 196 + 81

    289 = 277

    It is not a Pythagorean triple

    4) 8, 14, 16

    16² = 14² + 8² = 196 + 64

    256 = 260

    It is not a Pythagorean triple

    5) 8, 15, 17

    17² = 15² + 8²

    289 = 225 + 64

    289 = 289

    It is a Pythagorean triple

    Therefore, 3, 4,5 and 17, 15,8

    give the measures of the legs and hypotenuse of a right triangle.
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