(A) In Δ ABC, DE ∥ BC. If AD =x, DB =x-2, AE =x+2 and EC =x-1, then find the value of x.

Since \(\displaystyle \mathrm{DE} \| \mathrm{BC} \Rightarrow \frac{\mathrm{AD}}{\mathrm{DB}}=\frac{\mathrm{AE}}{\mathrm{EC}}\)

\[\Rightarrow \frac{x}{x-2}=\frac{x+2}{x-1} \]

Solving, we get \(\displaystyle x=4\)

\[\begin{aligned} & \Delta \mathrm{ABC} \sim \Delta \mathrm{XYZ} \Rightarrow \frac{\mathrm{AB}}{\mathrm{XY}}=\frac{\mathrm{BC}}{\mathrm{YZ}}=\frac{\mathrm{AC}}{\mathrm{XZ}} \\ & \Rightarrow \frac{4}{x}=\frac{6}{7.2}=\frac{y}{6} \end{aligned} \]

Solving, we get \(\displaystyle x=4.8 \mathrm{~cm}, y=5 \mathrm{~cm}\)