To answer the question above, we make use of the Pythagorean theorem which can be mathematically expressed as,
a² + b² = c²
There are 3 right triangles in the figure. ΔABC, ΔADB, and ΔBDC. The Pythagorean equations are,
ΔABC: (AB)² + m² = (11 + 7)²
ΔADB: 11² + (BD)² = (AB)²
ΔBDC: (BD)² + 7² = m²
We may use either substitution or elimination method to solve for AB, BD and m. The answer I got is 11.22.