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10 March, 04:11

The longest side of a right triangle is 15 feet. The third side is 15 less than three times the shortest side. Find the length of the shortest side.

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  1. 10 March, 04:29
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    Answer: The shortest side is 9ft

    Step-by-step explanation: If the longest side is identified as 15 ft, then we already have our hypotenuse (the longest side in a right angled triangle).

    If the shortest side is labelled as x, then the third side of the triangle would be labelled as 3x - 15 (15 less than three times the shortest side).

    Now we have three sides of a triangle which we can label as 15, x and 3x - 15

    By applying the Pythagoras theorem, AC² = AB² + BC²

    (Where AC is the hypotenuse and AB and BC are the other two sides)

    15² = X² + (3x-15) ²

    By expansion, (3x-15) ² becomes 9x² - 90x + 225

    Hence, 225 = X² + 9X² - 90X + 225

    225 = 10X² - 90X + 225

    Subtract 225 from both sides of the equation

    10X² - 90X = 0

    Factorize the left hand side of the equation by 10x

    10x (x - 9) = 0

    Therefore, either

    10x = 0 OR

    x - 9 = 0

    If 10x=0, then x=0. OR

    If x - 9 = 0, then x = 9

    The length of the shortest side is 9ft.
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