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18 January, 22:31

An art studio purchased a triangular plot of land in a town and constructed a new building whose base is in the shape of a right triangle. The two legs have lengths of xminus4 feet and x plus 6 feet. The hypotenuse is 2 minus 18 feet. Find the lengths of the three sides.

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  1. 18 January, 22:57
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    The sides are 30 ft, 40 ft and 50 ft.

    Step-by-step explanation:

    The length of the triangle are as follows x - 4, x + 6 and 2x - 18. The hypotenuse should be 2x - 18. The hypotenuse is the longest side of a right angle triangle.

    Using Pythagoras theorem the length of the sides can be found.

    a² + b² = c²

    (x - 4) ² + (x + 6) ² = (2x - 18) ²

    (x - 4) (x - 4) + (x + 6) (x + 6) = (2x - 18) (2x - 18)

    x² - 4x - 4x + 16 + x² + 6x + 6x + 36 = 4x² - 36x - 36x + 324

    2x² - 8x + 12x + 16 + 36 = 4x² - 72x + 324

    2x² + 4x + 52 = 4x² - 72x + 324

    2x² - 4x² + 4x + 72x + 52 - 324 = 0

    -2x² + 76x - 272 = 0

    2x² - 76x + 272 = 0

    divide through by 2

    x² - 38x + 136 = 0

    find the number you can multiply to give you 136 and add to give you - 38. The number are - 34 and - 4.

    x² - 4x - 34x + 136 = 0

    x (x - 4) - 34 (x - 4) = 0

    (x - 4) (x - 34) = 0

    x = 4 or 34

    we can only use 34 since using 4 will result to negative number.

    x - 4 = 34 - 4 = 30 ft

    x + 6 = 34 + 6 = 40 ft

    2x - 18 = 68 - 18 = 50 ft
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