Question

1. find the value of x in the figure below if \\(\overline{mp}\\) is parallel to \\(\overline{ra}\\).

figure is not necessarily drawn to scale.
\\(\circ\\) 20.5 units
\\(\circ\\) 18 units
\\(\circ\\) 4.5 units
\\(\circ\\) 5 units

Explanation:

Step1: Apply Triangle Proportionality Theorem

Since $\overline{MP} \parallel \overline{RA}$, the theorem gives $\frac{x}{18} = \frac{5}{20}$.

Step2: Simplify the right-hand side

$\frac{5}{20} = \frac{1}{4}$, so $\frac{x}{18} = \frac{1}{4}$.

Step3: Solve for x

Multiply both sides by 18: $x = 18 \times \frac{1}{4}$
$x = \frac{18}{4} = 4.5$

Answer:

4.5 units