MathDB

\vartriangle ABC

AB = 3

BC = 5

, and

CA = 6

. Points

D

and

E

are chosen such that

ACDE

is a square which does not overlap with

\vartriangle ABC

. The length of

BD

can be expressed in the form

\sqrt{m + n\sqrt{p}}

, where

m

n

, and

p

are positive integers and

p

is not divisible by the square of a prime. Determine the value of

m + n + p

Problem Statement