MathDB

Purple Comet 2017 HS problem 13

Source:

March 19, 2020

geometryperimeter

Problem Statement

Let

ABCDE

be a pentagon with area

2017

such that four of its sides

AB, BC, CD

, and

EA

have integer length. Suppose that

\angle A = \angle B = \angle C = 90^o

,

AB = BC

, and

CD = EA

. The maximum possible perimeter of

ABCDE

is

a + b \sqrt{c}

, where

a

,

b

, and

c

are integers and

c

is not divisible by the square of any prime. Find

a + b + c

.

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