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2 June, 13:33

A field in the shape of a right triangle has an area of 30 square meters. If one leg of the right triangle that forms the field is 4 meters longer than the other leg, what is the length of the longer leg?

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  1. 2 June, 13:43
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    Let S=length of shorter leg, then the longer leg measures S+4.

    Area of a right triangles = product of legs / 2 (in m.)

    and

    Area of given right-triangle = 30 m^2

    To find S, solve

    product of legs / 2 = S (S+4) / 2 = 30 = area of triangle

    S (S+4) = 2*30 [ now distribute ]

    S^2+4S = 60 [ subtract 60 from both sides ]

    s^2+4S-60=0

    Solve for S by factoring

    (S+10) (S-6) = 0 means (S+10) = 0 or (S-6) = 0

    Therefore S=6 or S=-10, reject negative root, so

    shorter leg = 6m

    longer leg = 6m+4m = 10m
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