Respuesta :

Since NK and NM are the same 14x-3 = 25. Add the 3 to 25 to get 14x = 28. Then divide 28 by 14 making x = 2. Now you know what x is, you can work out 9x + 5. 9 x 2 = 18 + 5 = 23 making KL = 23. KL and LM are equal so LM also equals 23
akposevictor

The length of segment LM which is congruent to segment KL in the figure given is 23.

Given:

  • KN = 14x - 3
  • MN = 25
  • KL = LM = 9x + 5

Let's find the value of x by creating an equation we can solve.

  • Thus:

KN = MN (congruent sides)

  • Substitute

[tex]14x - 3 = 25[/tex]

  • Add 3 to both sides

[tex]14x - 3 + 3 = 25 + 3\\\\14x = 28[/tex]

  • Divide both sides by 14

[tex]\frac{14x}{14} =\frac{28}{14}\\\\x = 2[/tex]

  • Find LM

LM = KL (congruent segments)

  • Substitute

[tex]LM = 9x + 5[/tex]

  • Plug in the value of x

[tex]LM = 9(2) + 5\\\\LM = 18+ 5\\\\LM = 23[/tex]

Therefore, the length of segment LM in the figure given is 23.

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