AIME I 2026 (Problem 14)

Plane GeometryHard

In an equiangular pentagon, the sum of the squares of the side lengths equals 308, and the sum of the squares of the diagonal lengths equals 800. The square of the perimeter of the pentagon can be expressed as

m\sqrt n

, where

m

and

n

are positive integers and

n

is not divisible by the square of any prime. Find

m+n