MathDB

Possible perimeters

Source:

May 11, 2006

geometryperimeterinequalitiestrigonometryperpendicular bisectorPythagorean Theorem

Problem Statement

Point

B

is on

\overline{AC}

with

AB = 9

and

BC = 21

. Point

D

is not on

\overline{AC}

so that

AD = CD

, and

AD

and

BD

are integers. Let

s

be the sum of all possible perimeters of

\triangle ACD

. Find

s

.

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