Not that easy to "explain"...I'll try:

label the 15 by 26 rectangle ABCD clockwise, A top left corner;

label end of line from D as E, end of line from C as F, so DE = CF = 39;

draw perpendicular EG, G on CF: so EG = x;

so we now have right triangles BCF and EGF: these are SIMILAR triangles

Since similar, then EG/EF = BC/CF : x/15 = 26/39 : x = 10