Question

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

Answer 1

C

Explanation:

Since BC is parallel to DF and intersects the other 2 sides then it divides those sides in proportion, that is

`(EB)/(BD)` =
`(EC)/(CF)` , substitute values

`(3)/(5x-4)` =
`(5)/(4x+2)` ( cross- multiply )

5(5x - 4) = 3(4x + 2) ← distribute parenthesis on both sides )

25x - 20 = 12x + 6 ( subtract 12x from both sides )

13x - 20 = 6 ( add 20 to both sides )

13x = 26 ( divide both sides by 2 )

x = 2

Thus

DE = 5x - 4 + 3 = 5(2) - 1 = 10 - 1 = 9

EF = 5 + 4x + 2 = 5 + 4(2) + 2 = 5 + 8 + 2 = 15