A polygon has 1325 diagonals. How many vertices does it have?

Ms Doe,

In a polygon, the number of vertices equals the number of sides it has, as you said, an octagon has eight, a rectangle has 4 etc. However, it does not have to be equal to TWICE the number of diagonals. A rectangle can have UP TO two diagonals, and an octagon can have UP TO 8x5/2=20 diagonals, as stated in the first two solutions.

The number of diagonals does not determine the number of vertices, but the number of vertices determine the MAXIMUM number of distinct diagonals one can draw within the polygon.
I go with the first two solutions.
Best regards.

Posted by P C on 2004-02-04 19:24:43