Let a and b be the leg lengths of a right triangle, and let c be the length of the hypotenuse. If all three are natural numbers, and a is an

Question

Let a and b be the leg lengths of a right triangle, and let c be the length of the hypotenuse. If all three are natural numbers, and a is an odd prime number, prove that the number 2(a+b+1) is a square of some natural number.

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King 3 years 2021-07-30T23:46:39+00:00 1 Answers 14 views 0

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  1. Sapo1
    0
    2021-07-30T23:48:10+00:00
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    Answer:

    this has been proven to be true

    Step-by-step explanation:

    from pythagoras theorem, we know that for any right angkd triangle

    a²+b² = c²

    if a is an odd number as well as a prime number,

    a= 3

    b = 4

    such that

    2(a+b+1) = 2(3+4+1) = 2 * 8 = 16

    16 is a square of 4.

    also if a = 5 and b = 2

    2(5+2+1) = 2*8 = 16

    16 is a square of 4

    so this has been proven to be true for the odd and prime numbers of a.

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