Write an expression in simplest form for the perimeter of a right triangle with leg lengths of 3a cubed and 4a cubed

Question

Write an expression in simplest form for the perimeter of a right triangle with leg lengths of 3a cubed and 4a cubed

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Clara 2 days 2021-10-13T03:55:40+00:00 1 Answer 0

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    2021-10-13T03:57:32+00:00

    Answer:

    106.4622 a^{3}

    Step-by-step explanation:

    Given the information:

    • A right triangle
    • Leg lengths of (3a)^{3} and (4a)^{3}

    Use the pytagon theory to find the hypotenuse of the triangle

    a^{2}  + b^{2}  = c^{2}

    <=>((3a)^{3}) ^{2}  + ((4a)^{3}) ^{2}  = c^{2}

    <=>(3a)^{6} + (4a)^{6} = c^{2}  

    <=> c^{2}  = 4285a^{6}

    Take the square root of both sides

    <=> c = 69.4622 a^{3}

    => expression in simplest form for the perimeter of a right triangle is:

    (3a)^{3} + (4a)^{3} + 69.4622 a^{3}  

    = 27a^{3}  + 64a^{3}  + 69.4622 a^{3}  

    = 106.4622 a^{3}

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