Question

1. if $ac = 18$ and $ab = 15$, find the value of $x$.

Explanation:

Step1: Assume similar - triangles

Since the two lines are parallel, the two triangles are similar. Let the smaller triangle have sides \(6\) and \(AC - 6=18 - 6 = 12\), and the larger triangle have sides \(AB = 15\) and \(BC\). By the property of similar - triangles, the ratios of corresponding sides are equal.

Step2: Set up the proportion

The ratio of the sides of the similar triangles gives \(\frac{6}{18}=\frac{15 - x}{15}\).
Cross - multiply: \(6\times15=18\times(15 - x)\).
Expand the right - hand side: \(90 = 270-18x\).

Step3: Solve for \(x\)

Add \(18x\) to both sides: \(18x + 90=270\).
Subtract \(90\) from both sides: \(18x=270 - 90=180\).
Divide both sides by \(18\): \(x = 10\).

Answer:

\(10\)