Find the lenghts of segments

Question

Find the length of each segment  DE, EF and DF

DE = 2x + 4

EF = 3x - 1

Answer 1

Given : DE = 2x + 4 and EF = 3x - 1.

E is the mid point of DF.

DE = EF

2x + 4 = 3x - 1

3x - 2x = 4 + 1

x = 5.

If, x = 5, then DE = 2x + 4 = 2(5) + 4 = 10 + 4 = 14.

EF = 3x - 1 = 3(5) - 1 = 15 - 1 = 14.

DF =  DE + EF = 14 + 14 = 28.