Answer:
The correct option is 7.5
Therefore the length of BE is 7.5 units
Step-by-step explanation:
Given:
AB || CD
AE = 5
DE = 2
EC = 3
DC = 1.5
To Find:
BE = ?
Solution:
In Δ ABE and Δ DCE
∠ABE ≅ ∠DCE …………..{ Alternate angles are equal since AB || CD }
∠AEB ≅ ∠DEC ……….....{Vertical opposite angles are equal}
Δ ABE ~ Δ DCE….{Angle-Angle Similarity test}
If two triangles are similar then their sides are in proportion.
[tex]\dfrac{BE}{CE} =\dfrac{AE}{DE}=\dfrac{AB}{DC} \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]
Substituting the values we get
[tex]\dfrac{BE}{CE} =\dfrac{AE}{DE}[/tex]
[tex]\dfrac{BE}{3}=\dfrac{5}{2}\\\\BE=\dfrac{15}{2}=7.5[/tex]
Therefore the length of BE is 7.5 units
