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21 March, 23:46

The area of a right triangle is 35m^2. The hypotenuse has a length of the square root of 149 m. What are the lengths of the legs? (one answer) ?

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  1. 22 March, 01:12
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    Area = 1/2 * product of the 2 legs

    let 2 legs be x and y m long. Then:-

    0.5xy = 35 ... (1)

    x^2 + y^2 = (sqrt149) ^2

    x^2 + y^2 = 149 ... (2)

    From equation (1) : - y = 35 / 0.5x = 70 / x

    Substituting in equation (2)

    x^2 + (70/x) ^2 = 149

    x^4 + 4900 = 149x^2

    x^4 - 149x^2 + 4900 = 0

    (x^2 - 100) (x^2 - 49) = 0

    x^2 = 100 or x^2 = 49

    x = 10, y = 7

    Lengths of the legs are 7 and 10 m Answer
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