Answer:
m = 4√6
Step-by-step explanation:
Using the "geometric mean" relations applicable to this triangle, the value of m is the geometric mean of the hypotenuse segments it touches:
m = √((8)(8+4)) = √96
m = 4√6
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Additional comment
Similarly, n = √(4×8) = 4√2.
These relations come from the similarity of the triangles. For m, the proportion is ...
long side/hypotenuse = 8/m = m/12
96 = m² ⇒ m = 4√6
