Question

AB is parallel to CD. What is the length of BE? 3.75 6 3.33 7.5

Answer 1

The correct option is 7.5

Therefore the length of BE is 7.5 units

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

∠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.

`(BE)/(CE) =(AE)/(DE)=(AB)/(DC) \textrm{corresponding sides of similar triangles are in proportion}\\`

Substituting the values we get

`(BE)/(CE) =(AE)/(DE)`

`(BE)/(3)=(5)/(2)\\\\BE=(15)/(2)=7.5`

Therefore the length of BE is 7.5 units