<PRE><B>Question 1019981</B>
{{{L}}}= length (in meters) of the longest side
{{{S}}}= length (in meters) of the shortest side (or one of the two shorter sides, if isosceles)
{{{M}}}= length (in meters) of the other side.
For that triangle to be obtuse, we need
{{{S^2+M^2&lt;L^2}}} .
 
If the {{{9}}} meter side is the longest side, and the length of the other side is {{{x}}} meters,
{{{x^2+7^2&lt;9^2}}}&lt;--&gt;{{{x^2+49&lt;81}}}&lt;--&gt;{{{x^2&lt;81-49}}}&lt;--&gt;{{{highlight(x^2&lt;32)}}} .
 
If the longest side is the unknown side, measuring {{{x}}} meters,
{{{7^2+9^2&lt;x^2}}}&lt;--&gt;{{{49+81&lt;x^2}}}&lt;--&gt;{{{highlight(x^2&gt;130)}}} .
 
{{{4^2=16&lt;32}}} so a 4 meter shortest side is an option;
{{{5^2=25&lt;32}}} so a 4 meter shortest side is an option;
{{{12^2=144&gt;130}}} so a 12 meter longest side is an option, but
{{{32&lt;11^2=121&lt;130}}} means that an obtuse triangle with sides measuring 7 and 9 meters cannot have a third side measuring {{{highlight(11meters)}}} .
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