Chef Ignacio liked to prop his two identical thin rectangular chopping boards against the shelf at the end of his counter to dry. He placed the top of the first one flush with the shelf corner and rested the second on the first, as shown in the diagram. To aid drying, he positioned the second to maximise the air volume in the bounded region below it. The length of each board is an even number of cm (less than 26cm) 
The distance between the bases of the two boards was a whole number of mm. What is this distance?
 and the height of the shelf above the counter is an integer number of millimetres.