Question

the length of $overline{df}$ is 35. find the length of $overline{de}$.
draw
$d$ -----$x + 2$-----$e$ -----$2x + 3$-----$f$
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Explanation:

Step1: Set up the equation

Since \( DF = DE + EF \), we have \( (x + 2) + (2x + 3) = 35 \).

Step2: Simplify the left side

Combine like terms: \( 3x + 5 = 35 \).

Step3: Solve for \( x \)

Subtract 5 from both sides: \( 3x = 30 \), then divide by 3: \( x = 10 \).

Step4: Find \( DE \)

Substitute \( x = 10 \) into \( DE = x + 2 \): \( DE = 10 + 2 = 12 \).

Answer:

12