Question

find the measure of (overline{de}).

Explanation:

Step1: Identify segment equality

Since \( CD = DE \) (marked congruent), set \( 2x + 7 = 4(x - 3) \).
\[ 2x + 7 = 4x - 12 \]

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides:
\[ 7 = 2x - 12 \]
Add 12 to both sides:
\[ 19 = 2x \]
Divide by 2:
\[ x = \frac{19}{2} = 9.5 \]

Step3: Calculate \( DE \)

Substitute \( x = 9.5 \) into \( 4(x - 3) \):
\[ 4(9.5 - 3) = 4(6.5) = 26 \]

Answer:

\( 26 \)