Questions: The diagram below includes similar quadrilaterals. Find the length of AB.

Transcript text: The diagram below includes similar quadrilaterals. Find the length of $\overline{A B}$.

Solution

Solution Steps

Step 1: Identify the Corresponding Sides

Since the quadrilaterals are similar, the corresponding sides are proportional. Identify the corresponding sides:

$ AB $ corresponds to $ EF $
$ BC $ corresponds to $ FG $
$ CD $ corresponds to $ GH $
$ DA $ corresponds to $ HE $

Step 2: Set Up the Proportion

Using the corresponding sides, set up the proportion: \[ \frac{AB}{EF} = \frac{BC}{FG} = \frac{CD}{GH} = \frac{DA}{HE} \]

Step 3: Substitute Known Values

Substitute the known values into the proportion: \[ \frac{AB}{8} = \frac{7.5}{4} = \frac{6}{6} = \frac{9}{6} \]

Step 4: Solve for $ AB $

Use the proportion involving $ AB $ and $ EF $: \[ \frac{AB}{8} = \frac{9}{6} \] \[ AB = 8 \times \frac{9}{6} \] \[ AB = 8 \times 1.5 \] \[ AB = 12 \]

Final Answer

The length of $ AB $ is $ 12 $.

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