Question

How do I solve this problem

Answer 1

$\overline{LK}\cong\overline{MK}\\LK=MK=7x-10\\KN=x+3\\MN=9x-11\\KJ=28\\\\MN=MK+KN\\\text{therefore we have the equation:}\\9x-11=(7x-10)+(x+3)\\9x-11=8x-7\ \ \ |+11\\9x=8x+4\ \ \ \ |-8x\\x=4$

$LJ=LK+KJ\\\\LK=7x-10\to LK=7(4)-10=28-10=18\\\\\text{therefore}\\LJ=18+28=46$

Answer: LJ = 46.