2P ΔAPL = 30
1) Let's calculate the 2P of triangle APL
Since we have in P the incenter of the triangle, and three medians there is a ratio of 2:1 between the segments of each median.
The incenter implies that there is a circumference inside the triangle so
JP≅ PL ≅PK because these are the radius of that circumference
T
hen PL
13² = AL²+5² Pythagorean theorem
169=AL² +25
169-25= AL²
AL = 12
AL = 12 then AC = 6 Median ratio
AJ = 12 then JB = 6 Median ratio
Then we have isosceles triangles inside what allows us to write
So the Perimeter of ABC is:
2P = 18 +18 +12
2P = 36+12
2P =48
And the Perimeter of APL is 2P = 12 +13 +5
ΔAPL = 12 +18
2P ΔAPL = 30