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25 January, 01:13

One side of a right triangle is 2 cm shorter than the hypotenuse and 7 cm longer than the third side. find the lengths of the sides of the triangle.

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  1. 25 January, 01:54
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    The right angles triangle has three sides including the hypotenuse which is opposite to the right angle.

    If the hypotenuse - H

    Then one side is - H - 2

    Third side is 7 cm shorter then H-2

    Therefore it’s H - 2-7 = H - 9

    According to Pythagoras theorem

    Square of hypotenuse = sum of the squares of the other 2 sides

    H² = (H-9) ² + (H-2) ²

    H² = H² - 18H + 81 + H² - 4H + 4

    0 = H² - 22H + 85

    This is a quadratic equation

    0 = H² - 17H - 5H + 85

    0 = H (H - 17) - 5 (H-17)

    (H-17) (H-5) = 0

    H - 17=0 or H-5=0

    H could be 17 cm or 5 cm

    If H = 5 cm then

    Side 1 - H-2 = 3 cm

    And side 2 - H-9 = - 4 cm

    Since lengths cannot be negative values

    H isn’t 5 cm

    Therefore H = 17 cm

    1 side is H-2 = 15 cm

    2nd side H - 9 = 8 cm

    Three sides are 17 cm, 15 cm and 8 cm
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