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    maalcosxiejohn's Avatar
    maalcosxiejohn Posts: 1, Reputation: 1
    New Member
    		  
    #1

    Sep 27, 2010, 03:50 AM
    solving problems involving quadratic equation
    One leg of right triangle is 2cm more than the other the hypotenuse is10cm find the measure of the two legs
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
    Uber Member
    		  
    #2

    Sep 27, 2010, 04:15 AM

    Make a drawing...

    Code:
           /|
      / |
     /  |
    /   |
10 /    | x+2
  /     |
 /      |
/_______|
    x
    Let's call the shorter length x and the longer one x+2, while the hypotenuse is 10.

    Using Pythagoras' Theorem, we know that:



    Can you solve this quadratic now? :)
    BillRussell's Avatar
    BillRussell Posts: 8, Reputation: 1
    New Member
    		  
    #3

    Sep 30, 2010, 12:54 PM
    Let x be the first leg
    x + 2 is the second
    hyp² = 10² = (x² + (x+2)²)
    100 = x² + x² + 4x + 4
    2x² + 4x – 96 = 0
    x² + 2x – 48 = 0
    factor
    (x – 6)(x + 8) = 0
    x = 6, –8
    skipping the negative answer, we have
    x = 6

    checking
    leg 1 = 6
    leg 2 = 8
    h = √(6² + 8²)
    OK

    b
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