Question

What’s the length of E to D
what’s the length of B to E

Answer 1

Given:

In triangle ACD, BE||CD, AB = 20 cm, BC = 5 cm, CD = 18 cm, AE = 26 cm.

To find:

(a) The length of ED.

(b) The length of BE.

Solution:

In triangle ABE and ACD,

BE||CD, so angle ABE and angles ACD are corresponding angles. So, their measure are equal.

`m\angle ABE=m\angle ACD` (Corresponding angles)

`m\angle BAE=m\angle CAD` (Common angle)

Now,

`\Delta ABE\sim \Delta ACD`

Corresponding sides of similar triangles are proportional.

`(AB)/(AC)=(BE)/(CD)=(AE)/(AD)`

(a)

`(AB)/(AC)=(AE)/(AD)`

`(20)/(20+5)=(26)/(AD)`

`(20)/(25)=(26)/(AD)`

`0.8=(26)/(AD)`

Isolate AD.

`0.8AD=26`

`AD=(26)/(0.8)`

`AD=32.5`

Now,

`AD=AE+ED`

`32.5=26+ED`

`32.5-26=ED`

`6.5=ED`

Therefore, the length of ED is 6.5.

(b)

`(AB)/(AC)=(BE)/(CD)`

`(20)/(25)=(BE)/(18)`

`0.8=(BE)/(18)`

Multiply both sides by 18.

`14.4=BE`

Therefore, the length of BE is 14.4.