As shown in the figure. In order to make EFGH a diamond, we must first ensure that EH=FG.

Such as EH=ED+DH=DP+DQ=2DP+DQ.

Similarly FG=FB+BG=BP+BQ=2BQ+PQ.

So from EH=FG: 2BQ+PQ=2DP+PQ.

So BQ=DP. This paper guarantees that EH=FG and EH//FG are known, so EFGH is a parallelogram.

Now let BQ = DP = X. Then DE=x, DH = DQ = 5-X. So EH=ED+DH=5.

EP=8x/5，PF=6(5-x)/5 .

EFGH is a diamond, then EF=EH.

According to Pythagorean theorem EP 2+PF 2 = EF 2 = EH 2

Solve the equation: x=2.5 or 1. 1.

When x=2.5, PQ=0, which is irrelevant.

So x= 1. 1, PQ=5-2x=2.8.