Is 9, 12, 15 the lengths of the sides of a right triangle? (Show work)​

Question

Is 9, 12, 15 the lengths of the sides of a right triangle? (Show work)​

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Elliana 3 days 2021-10-14T00:35:08+00:00 2 Answers 0

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    0
    2021-10-14T00:36:22+00:00

    Answer:

    Yes, the triangle lengths 9, 12, and 15 are lengths of the sides of a right triangle.

    Step-by-step explanation:

    There are multiple different ways to prove that this answer is correct.

    To begin, we could recognize that these side lengths are a Pythagorean triple, or multiples of side lengths that satisfy the Pythagorean theorem, and thus prove that the lengths constitute a right triangle. In this case, 9, 12, and 15 represent the 3, 4, 5 Pythagorean triple where each side length is multiplied by a factor of three.

    3×3=9

    4×3=12

    5×3=15

    Therefore, these side lengths do make a right triangle because they represent a multiple of a Pythagorean triple.

    If we didn’t recognize this, we could always plug the side lengths into the Pythagorean theorem, a^2 + b^2 = c^2.

    In this case, we get

    9^2 + 12*2 = 15^2

    If we simplify, we get:

    81+144 = 225

    And if simplified further, we get:

    225=225,

    Which is a true statement, proving that these side lengths do make up a right triangle.

    Hope this helps!

    0
    2021-10-14T00:36:48+00:00

    Hello There!

    To find out if these lengths make a triangle, you have to add up any two sizes and they must be greater than the third side for it to form a triangle.

    Let’s Test It!

    “9+12=21” 21 is greater than 15

    “9+15=24” 24 is greater than 12

    Yes This Does Form A Triangle!

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