Question

Find the lengths of DE and EF. Note: Segments BC and DF are parallel.

Answer 1

c-de=9cm; ef=15cm hope this helps

Answer 2

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.

$\frac{EB}{ED}=\frac{EC}{EF}$

$\frac{3}{(5x-4)}=\frac{5}{4x+2}$

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.