Quote:
The length of one of the sides of a triangle is 25 units. If the area of the triangle is 120 units squared and the length of another side of the triangle is 10 units, which of the following could be the length of the third side?
A) \(\sqrt{255}\)
B) \(\sqrt{585}\)
C) \(\sqrt{572}\)
D) \(\sqrt{558}\)
E) 24
\(? = x\)
\(\left\{ \begin{gathered}
\,{x^2} = {\left( {10 + 7} \right)^2} + {24^2} = 289 + 576\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,x = \sqrt {865} \hfill \\
\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{OR}} \hfill \\
\,{x^2} = {24^2} + {3^2} = 576 + 9\,\,\,\, \Rightarrow \,\,\,\,x = \sqrt {585} \hfill \\
\end{gathered} \right.\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
_________________
Fabio Skilnik ::
GMATH method creator (Math for the GMAT)
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