The two smaller pieces DE and EF combine to form segment DF.
We'll use this fact to set up the equation below and solve for w.
DE + EF = DF
(4w) + (3w+14) = 63
7w+14 = 63
7w = 63-14
7w = 49
w = 49/7
w = 7
Use this value of w to find DE and EF:
- DE = 4w = 4*7 = 28
- EF = 3w+14 = 3*7+14 = 21+14 = 35
In short,
- DE = 28 inches
- EF = 35 inches
As a check: DE + EF = 28+35 = 63, which confirms we have the correct answers.