Summer Problem Solving Marathon Solution #30

Diagonal AC is the hypotenuse of right triangle ABC, with legs 18 and 21. So AC is √(18² + 21²) = &radic(324 + 441) = √765.

AD is then the hypotenuse of right triangle ACD, with legs 14 and √765. AD is thus √(14² + 765) = √(196 + 765) = √961 = 31.

The perimeter of ABCD is thus 18 + 21 + 14 + 31 = 84.