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Geometry Level 2

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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