Question 2: \( \triangle A B C \cong \triangle D E F, B C=3 p+18 \), and \( E F=5 p-4 \). Find \( p \) and \( E F \).
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Since \( \triangle A B C \cong \triangle D E F \), their corresponding sides are equal. Therefore, we can set up the equation: \[ BC = EF \] Substituting the expressions for \( BC \) and \( EF \): \[ 3p + 18 = 5p - 4 \] Now, we can solve for \( p \). First, rearrange the equation: \[ 18 + 4 = 5p - 3p \] \[ 22 = 2p \] Now, divide both sides by 2: \[ p = 11 \] Next, we substitute \( p \) back into the expression for \( EF \): \[ EF = 5p - 4 = 5(11) - 4 = 55 - 4 = 51 \] Therefore, \( p = 11 \) and \( EF = 51 \).