Question

DEllAC AD=BE AB=16 BC=24
BE-? BD-?

Answer 1

BE = 3.6 units

BD = 12.4 units

Explanation:

From the picture attached,

Since DE║AC, ΔBDE and ΔABC will be similar.

In these similar triangles corresponding side will be in the same ratio.

`(BD)/(AB)=(BE)/(BC)`

`(AB-AD)/(AB)=(BE)/(BC)`

`1-(AD)/(AB)=(BE)/(BC)`

1 -
`(BE)/(AB)=(BE)/(BC)` [Since AD = BE]

1 -
`(BE)/(16)=(BE)/(24)`

1 =
`(BE)/(16)+(BE)/(24)`

1 =
`BE((3+2)/(48))`

BE =
`(18)/(5)`

BE = 3.6 units

Therefore, AD = BE = 3.6 units [given]

Now BD = AB - AD

= 16 - 3.6

= 12.4 units