Using the provided diagram and lengths, determine the length of EG.

Here are the solutions to the problems.

QUESTION 10

• 10.1 Determine EG

  Step 1: Identify parallel lines and transversals.
  Given $DE \parallel FG \parallel BC$. Lines $AB$ and $AC$ are transversals.

  Step 2: Apply the Proportionality Theorem (Thales's Theorem) to transversals $AB$ and $AC$ cut by parallel lines $DE$ and $FG$.

  $$\frac{AD}{DF} = \frac{AE}{EG}$$

  Step 3: Substitute the given values $AD = 36$ cm, $DF = 24$ cm, $AE = 48$ cm.

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