2015 HCI P1 Q3

A tunnel is built to facilitate the transportation of goods by trains between Country \(\mathrm{X}\) and Country \(\mathrm{Y}\). Due to differences in the rail systems between the two countries, two types of tracks are used – the international track with track gauge of \(1435\) mm and the narrow track with track gauge of \(1000\) mm (in rail transport, track gauge is the spacing on a railway track). It is known that the cross-section of the tunnel is a half ellipse with centre \(O\) and width \(MN\) (see diagram). The maximum height of the tunnel is \(2000\) mm. To standardize the volumes of the goods to be transported, the areas \(ABCD\) and \(EFGH\) are made equal. Find the width of the tunnel \(MN\), giving your answer to the nearest mm.[4]