A storeroom has a floor 16 m long and 12 m wide, and the longest straight rod that can be placed anywhere inside it measures 25 m. How high is the storeroom, in metres?

The longest rod lies along the space diagonal, so $l^2+b^2+h^2=25^2$: that is $256+144+h^2=625$, giving $h^2=225$ and $h=15$ m. The trap 19.21 = √(625 - 256) leaves the breadth out of the sum; 3 = 25 - 16 - 12 subtracts the floor's sides from the rod as though the diagonal were a straight total of lengths; 12.5 simply halves the rod.