I was browsing the AMC 2010 Brochure, and came across problem

10A-12, 12A10. It it possible to solve this problem with the given information? If so, how? Thanks in advance.

- November 15th 2009, 01:03 PMasyed94Lenght of the Diagonal of a Quadrilateral given its 4 Side Lengths.
I was browsing the AMC 2010 Brochure, and came across problem

10A-12, 12A10. It it possible to solve this problem with the given information? If so, how? Thanks in advance. - November 15th 2009, 02:53 PMSoroban
Hello, asyed94!

It's much easier thank you imagine . . .

Quote:

In quadrilateral

And the length of diagonal is an integer.

Find the length of

Code:`A`

o

9 * *

* *

D * *

o * 5

* * *

5 * * *

* * *

C o * * * * * * o B

17

In , the Triangle Inequality says: .

That is: .

In , the Triangle Inequality says: .

That is: .

Therefore: is an integer between 12 and 14 . . .

- November 15th 2009, 03:17 PMasyed94
Many thanks for the quick and concise reply. This problem had me on the ropes all day :). How were you able to determine the method necessary to solve it?