Because both parts of the triangle are right triangles, you can solve this one by using the Pythagorean theorem (a² + b² = c²).  First, start with the triangle on the left:

(3m)² + (3m)² =  c²
9m² + 9m² = c²
18m² = c²
(3 square root2) m = c

The line segment AB = 18m.
Now use the same method to figure out the hypotenuse of the triangle on the right:

(3m)² + (4m)² =  c²
9m² + 16m² = c²
25m² = c²
5m = c

The line segment BC = 25 m.

Now add AB+BC+AC:

(3 square root2) m + 5m + 7m = 12m + (3 square root2) m
 

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