Since triangles ΔABC and ΔDEF are similar, the ratios of the lengths of corresponding sides are equal. We can set up a proportion using the sides BC and EF, and we want to find the measure of AB.
Given:
- \( BC = 36 \)
- \( EF = 3 \)
- \( DE = 6 \)
First, we can find the ratio of the sides BC and EF:
\[ \frac{BC}{EF} = \frac{36}{3} = 12 \]
This means that the corresponding sides also have a ratio of 12:1. Now, we can use this ratio to find the measure of AB corresponding to DE.
Since \( DE \) corresponds to \( AB \):
\[ \frac{AB}{DE} = \frac{AB}{6} = 12 \]
Now, we can solve for \( AB \):
\[ AB = 12 \times DE = 12 \times 6 = 72 \]
Thus, the measure of \( AB \) is \( 72 \).
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