The parallelogram contains two congruent triangles HOE and POL. Angles HOE and POL are equal, angles HEO (equal and opposite angles) and angles HEO=OPL and EHO=OLP (alternate angles). The diagonals of a parallelogram bisect one another, so PO=OE=4. HO=OL=1/2(HL). HL=PE+7=PO+OE+7=8+7=15. So HO (OH)=15/2=7.5 or 7 1/2.