Question

in the diagram below, \\( \overline{op} \\) is parallel to \\( \overline{lm} \\). if \\( op = 1.8 \\), \\( lm = 3 \\), and \\( on = 3 \\), find the length of \\( \overline{ln} \\). figures are not necessarily drawn to scale.

Explanation:

Step1: Define variable for LO

Let $LO = x$, so $LN = x + 3$.

Step2: Apply Basic Proportionality Theorem

Since $\overline{OP} \parallel \overline{LM}$, $\frac{OP}{LM} = \frac{ON}{LN}$
$\frac{1.8}{3} = \frac{3}{x+3}$

Step3: Solve for x

Cross-multiply: $1.8(x+3) = 3 \times 3$
$1.8x + 5.4 = 9$
$1.8x = 9 - 5.4$
$1.8x = 3.6$
$x = \frac{3.6}{1.8} = 2$

Step4: Calculate LN

$LN = x + 3 = 2 + 3$

Answer:

5