Question

Find JL. (relationships in triangles)

Answer 1

well, let's notice that JM = MK, KN = NL, because of those tickmarks, that simply means that the segment MN is the midsegment of the triangle, and the midsegment of a triangle is half of the parallel base, namely

`\bf \stackrel{MN}{5x-16}~~=~~\stackrel{half~JL}{\cfrac{4x+34}{2}}\implies 10x-32=4x+34\implies 6x-32=34 \\\\\\ 6x=66\implies x=\cfrac{66}{6}\implies x=11 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{JL}{4x+34}\implies 4(11)+34\implies \stackrel{JL}{78}`