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11 January, 04:42

The shorter leg of a right triangle is 21 feet less than the other leg. Find the length of the two legs if the hypotenuse is 39 feet.

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  1. 11 January, 05:10
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    leg 1 = 36 feet

    leg2 = 15 feet

    Step-by-step explanation:

    Hi, we have to apply the Pythagorean Theorem:

    c^2 = a^2 + b^2

    Where c is the hypotenuse of the triangle (in this case the distance between Doreen's house and the tower) and a and b are the other legs.

    leg1 = x

    leg2 = x-21 (21 feet less than the other leg)

    Replacing with the values given:

    39^2 = x^2 + (x-21) ^2

    1,521 = x^2 + x^2 - 42x + 441

    0 = 2x^2 - 42x + 441-1,521

    0 = 2x^2 - 42x - 1,080

    For: ax2 + bx + c

    x = [ - b ± √b²-4ac] / 2a (quadratic formula)

    Replacing with the values given:

    x = - (-42) ± √ (-42) ²-4 (2) - 1080] / 2 (2)

    x = 42± √10,404] / 4

    x = 42± 102 / 4

    Positive:

    x = 42+102 / 4 = 36

    leg 1 = 36

    leg2 = 36-21 = 15

    Feel free to ask for more if needed or if you did not understand something.
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