The two larger angles of an isosceles triangle have a combined measure of $135^\circ$. If this triangle has a perpendicular height of $2\text{ m}$, find the length of its base in meters.

If the latter can be expressed in the form $a\sqrt { b } -c$, where $a,b$ and $c$ are positive integers with $b$ square-free, write your answer as $a\times b\times c$.

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