Question

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

Answer 1

Answer:

LN = 15

Step-by-step explanation:

The arrows on the line segments indicate they are parallel.

$\implies \overline{KM} \parallel \overline{JN}$

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.

$\textsf{If }\overline{KM} \parallel \overline{JN}, \textsf{ then }\dfrac{LK}{LJ}=\dfrac{LM}{LN}$

Given:

• LM = 6
• JL = 30
• JK = 18

⇒ LK = JL - JK = 30 - 18 = 12

Substituting the values into the equation and solving for LN:

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

Answer 2

Answer: LN = 15

Make a proportional relationship:

$\sf \dfrac{LN}{JL} = \dfrac{LM}{KL}$

Insert the values:

$\rightarrow \sf \dfrac{LN}{30} = \dfrac{6}{30-18}$

cross multiply:

$\rightarrow \sf LN = \dfrac{30(6)}{12}$

Simplify:

• $\sf LN =15$