Figure ABCD is a rectangle. The length of segment AE is (2x + 1) units and the length of segment EC is (x + 7) units.

What is the length of diagonal BD?

Question

Figure ABCD is a rectangle. The length of segment AE is (2x + 1) units and the length of segment EC is (x + 7) units. 
 

 
What is the length of diagonal BD?

anonymous · Answer

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aroub · Answer

The diagonals of a rectangle are always congruent. 

So, AE=EC 

and they gave the length of each one:

AE= 2x+1 and EC=x+7 

Now just substitute and solve:

AE=EC
2x+1=x+7 
2x-x=7-1
x=6 

If half of the diagonal is 6 what should the other half be? 6 

6+6=12 

=> BD=12

anonymous · Answer

oh ty very much, but one question. How do i know which side to work on first ?

anonymous · Answer

cause also 12 is not an answer

aroub · Answer

Oh! Sorry, the length of one of them is 13 so: 13+13=26 

6 is for x, they don't want x.

anonymous · Answer

Oh ok, thank you! If i could give you another medal i would!:)

aroub · Answer

26 is an answer right? 

& you're welcome!

anonymous · Answer

Yes it is thanks!