Answer:
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.
[tex]\frac{EB}{ED}=\frac{EC}{EF}[/tex]
[tex]\frac{3}{(5x-4)}=\frac{5}{4x+2}[/tex]
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.
