There is a survey [article][1] by Berndt, Choi, and Kang devoted to the set of 58 Ramanujan's problems. Many of the problems have generated serious research activity since they were republished  in *Ramanujan's Collected Papers* in 1927.

An elementary solution to the specific geometric problem you've mentioned can be found in *Ramanujan's Notebooks, Part III* by Berndt (Springer, 1991, pp. 244-246). 
 






  [1]: http://docs.google.com/viewer?a=v&q=cache%3AffWlq0vofzIJ%3Aciteseerx.ist.psu.edu/viewdoc/download?doi%253D10.1.1.39.9228%2526rep%253Drep1%2526type%253Dpdf+Journal+of+the+Indian+Mathematical+Society+ramanujan&hl=en&gl=ua&pid=bl&srcid=ADGEESi13Ln1u-wrtp7LEv-etNY0aRzCjrGrpSAjF40NXDXrRcOXk4vmPVHBqL76LdmK4QIJzyF_VUMgUjcII08WKg3aoywJWNl8NYIAr_tOMb_DDmFEKjebj-ENKkTncTppPsERbeO2&sig=AHIEtbSq2qlNnVPmtxyvw2l3O-OpThAcpQ&pli=1