In the picture below, ABFG and BCDE are squares and their each one sides measures, respectively, a and b. Knowing that $\;\overline{AG}\,=\,\overline{CD}\,+\,2\;\,$ and the perimeter of the triangle ACG is 12, we can assure that a e b are both inside the interval:
The lantern shown in the picture is suspended by two strings perpendicular to each other. Knowing the length of each string is 1/2 and 6/5, respectively, what is the distance between the lantern and the ceiling?