Question 123863

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Discussion
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We need to use the formula for the area of a triangle {{{A=(bh)/2}}}, and the
fact that the base and the height can be described one in terms of the other.
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Solution
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Let the short leg be x, and then the longer leg would be 2x + 8.


We are given that the area of the triangle is {{{96cm^2}}}, so 

{{{(x(2x+8))/2=96}}}


{{{2x^2+8x=192}}}


{{{2x^2+8x-192=0}}}


{{{x^2+4x-96=0}}}


{{{(x+12)(x-8)=0}}}


{{{x=-12}}} or {{{x=8}}}


Since a triangle leg with a negative length measure doesn't make much sense,
exclude the negative value.  The short leg measures 8, therefore the long leg
measures {{{2(8)+8=24}}}
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Check Answer
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{{{(24*8)/2=96}}}.  Answer checks.
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