Homework Help

Solve for x

user profile pic

novjb | Salutatorian

Posted September 12, 2013 at 4:39 PM via web

dislike 0 like

Solve for x

Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)

Tagged with geometry, math

1 Answer | Add Yours

user profile pic

tiburtius | High School Teacher | (Level 3) Associate Educator

Posted September 12, 2013 at 6:15 PM (Answer #1)

dislike 0 like

First let's call the vertex between D and C E and the one between A and D (next to x) F.

`/_CDE=/_ADF` 

`/_CED=/_DFA=90^o`

And since the sum of angles in a triangle is constant (equal to 180°) it follows that the third angles are also equal that is

`/_ECD=/_DAF`

Now since all three angles are equal it follows that the triangles CDE  and AFD are similar, hence their sides must be proportional so we have

`|AD|:|DC|=x:|CE|`

Since ABCE is parallelogram `|AB|=|CD|=>|AB|=7.5`  also `|AB|=|DC|=>|DC|=5`

So we have

`7.5:5=x:4`

`5x=30`

`x=6`   <-- Your solution

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes