Find the lengths of de and ef. note: segments bc and df are parallel.
a) de = 7 cm; ef = 5 cm
b) de = 10 cm; ef = 6 cm
c) de = 9 cm; ef = 15 cm
d) de = 19.6 cm; ef = 18 cm

Option C is the answer.

Step-by-step explanation:

In the given triangles DEF and BCE sides DE and EF are parallel and DE and FE are transverse.

Since ∠ECB = ∠EFD (corresponding angles) and ∠EBC = ∠EDF (corresponding angles) and ∠E is common in both the triangles EBC and EDF.

Therefore ΔBCE and ΔDEF are similar.

Since these triangles are similar so their corresponding sides will be in the same ratio.

3(4x+2) = 5(5x-4)

12x + 6 = 25x -20

25x - 12x = 20 + 6

13x = 26

x = 2

Side DE = 5x - 4 + 3 = 5x - 1 = 5×2 - 1 = 10 - 1 = 9 cm

and EF = 4x + 2 + 5 = 4x + 7 = 4×2 + 7 = 8 + 7 = 15 cm

Option C is the answer.