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P is the centroid of △JLN, LO⊥JN, ∠NJK≅∠JNM, OP=8, OJ=15. Find the perimeter of △JLN.
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Apr 27, 2019
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P is the centroid of △JLN, LO⊥JN, ∠NJK≅∠JNM, OP=8, OJ=15. Find the perimeter of △JLN.
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Teodor Kurtev
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the complete question in the attached figure
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
JL
²=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
the answer is
the perimeter of △JLN is
86.6 units
Tanner Dolby
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May 3, 2019
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Tanner Dolby
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