When 2 lines are congruent, it means the lines have an equal or the same length. The length of LJ is 32 units
Given that:
[tex]LK = 7x - 10[/tex]
[tex]KN = x + 3[/tex]
[tex]MN = 9x - 11[/tex]
[tex]KJ = 28[/tex]
First, we calculate MK
[tex]MK = MN - KN[/tex]
So, we have:
[tex]MK = 9x - 11 - (x + 3)[/tex]
Open bracket
[tex]MK = 9x - 11 - x - 3[/tex]
Collect like terms
[tex]MK = 9x - x - 11 - 3[/tex]
[tex]MK = 9x - 14[/tex]
Given that: [tex]LK = MK[/tex]
This gives:
[tex]7x -10 = 9x - 14[/tex]
Collect like terms
[tex]9x - 7x = 14-10[/tex]
[tex]2x =4[/tex]
Divide both sides by 2
[tex]x =2[/tex]
The length of LJ is:
[tex]LJ = LK + KJ[/tex]
This gives:
[tex]LJ = 7x -10 + 28[/tex]
Substitute 2 for x
[tex]LJ = 7 \times 2 -10 + 28[/tex]
[tex]LJ = 14 -10 + 28[/tex]
[tex]LJ = 32[/tex]
Hence, the length of LJ is 32 units
Read more about congruent lines at:
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