we know that The Centroid of a Triangle is the point where the three medians of the triangle intersect. Each median divides the triangle into two smaller triangles of equal area. and the centroid divides each median into two segments whose lengths are in the ratio 2:1, with the longest one nearest the vertex
therefore
triangles LOJ and LON are similar ON=OJ=15 units then NJ=15+15-------> NJ=30 units
Let x--------> distance OL so OP=x/3 OP=8 x/3=8--------> x=8*3---------> x=24 units OL=24 units
in the right triangle JLO OJ=15 units OL=24 units JL=? applying the Pythagorean Theorem JL²=OJ²+OL²--------> JL²=15²+24²------> JL=28.30 units perimeter of triangle JLN P=JL*2+NJ-------> P=2*28.30+30------> P=86.60 units------> P=86.6 units
