Rdesmanglesidn
Answered

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If JL = 30, JK = 18, and LM = 6, then the value of LN is:

If JL 30 JK 18 And LM 6 Then The Value Of LN Is class=

Sagot :

Fieryanswererftidn

Answer: LN = 15

Make a proportional relationship:

[tex]\sf \dfrac{LN}{JL} = \dfrac{LM}{KL}[/tex]

Insert the values:

[tex]\rightarrow \sf \dfrac{LN}{30} = \dfrac{6}{30-18}[/tex]

cross multiply:

[tex]\rightarrow \sf LN = \dfrac{30(6)}{12}[/tex]

Simplify:

  • [tex]\sf LN =15[/tex]
Semsee45idn

Answer:

LN = 15

Step-by-step explanation:

The arrows on the line segments indicate they are parallel.

[tex]\implies \overline{KM} \parallel \overline{JN}[/tex]

Triangle Proportionality Theorem

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then it divides these two sides proportionally.

[tex]\textsf{If }\overline{KM} \parallel \overline{JN}, \textsf{ then }\dfrac{LK}{LJ}=\dfrac{LM}{LN}[/tex]

Given:

  • LM = 6
  • JL = 30
  • JK = 18

⇒ LK = JL - JK = 30 - 18 = 12

Substituting the values into the equation and solving for LN:

[tex]\begin{aligned}\implies \dfrac{LK}{LJ} & = \dfrac{LM}{LN}\\\\\dfrac{12}{30} & = \dfrac{6}{LN}\\\\12LN & = 30 \cdot 6\\\\LN & = \dfrac{180}{12}\\\\LN & = 15\end{aligned}[/tex]

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