1987 AIME Problem 6

Rectangle ABCD is divided into four parts of equal area by five segments as shown in the figure, where XY = YB + BC + CZ = ZW = WD + DA + AX, and PQ is parallel to AB. Find the length of AB (in cm) if BC = 19 cm and PQ = 87 cm.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.