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14 February, 20:29

One leg of a right triangle is 6in more than twice the length of the other leg. The hypotenuse is 9in more than the shorter leg. Find the lengths of all sides.

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  1. 14 February, 23:15
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    a=2.69 in

    b=11.37 in

    c=11.69 in

    Explanation:

    If we mark shorter side as a, we can write all sides expressed through a.

    So:

    - short side is a

    - longer side is 6 in longer then twice the length of short side b = 2a + 6

    - hypotenuse is 9 in longer then short leg c = a + 9

    Now we can write the Pythagoras theorem a^2 + b^2 = c^2 as:

    a^2 + (2a + 6) ^2 = (a + 9) ^2

    a^2 + 4a^2+24a+36 = a^2+18a+81

    When we solve this, we get:

    4a^2 + 6a - 45 = 0

    Now we have a quadratic equation which can be solved as:

    x = - b ± √ (b^2 - 4ac) / 2a

    When we plug in the values, we get that x equals 2.69 or - 4.19

    It's obvious that length of a side can not be negative, which means that a = 2.69 in.

    Side b is 2a + 6, which is 11.37 and c is a + 9 which is 11.69 inches.

    These are lengths rounded to two decimals so due to this approximation they may not be completely precise.
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