Problem:
In quadrilateral ABCD,∠B is a right angle, diagonal AC is perpendicular to CD, AB=18,BC=21, and CD=14. Find the perimeter of ABCD.
Solution:
Because AB2+BC2=AC2 and AC2+CD2=DA2, it follows that DA2=AB2+ BC2+CD2=182+212+142=961, so DA=31. Then the perimeter of ABCD is 18+21+14+31=84​.
The problems on this page are the property of the MAA's American Mathematics Competitions