Question

\\\frac{ab}{ac} = \frac{ae}{ad} = \frac{bc}{cd}\\
\\\frac{3}{w} = \frac{x}{2} = \frac{4}{6}\\
\\w = 4.5, \quad x = \\

Explanation:

Step1: Identify the given proportions

The image shows the ratios:

$$\frac{AB}{AC} = \frac{AE}{AD} = \frac{BC}{CD}$$

Substituting the given values:

$$\frac{3}{w} = \frac{x}{2} = \frac{6}{4}$$

Step2: Solve for \(w\) using the first and third ratios

$$\frac{3}{w} = \frac{6}{4}$$

$$6w = 12 \implies w = 2$$

(Note: The image states \(w = 1.5\), which appears to be a calculation error in the handwritten note, but we need to find \(x\)).

Step3: Solve for \(x\) using the second and third ratios

$$\frac{x}{2} = \frac{6}{4}$$

$$4x = 12 \implies x = 3$$

Alternatively, if we use the handwritten value \(w = 1.5\) to find \(x\) from the first two ratios:

$$\frac{3}{1.5} = \frac{x}{2} \implies 2 = \frac{x}{2} \implies x = 4$$

Answer:

\(x = 4\)