Thread: Lenght 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.

Hello, asyed94!

It's much easier thank you imagine . . .

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 . . .

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?