So PF=2/3

Because PE∨BC

So △ABM∽△APF

So AM/BM=AP/PF

The solution is AP=2.

Make EF=EG

Need to make < ∠EFG =∠ < epidermal growth factor.

That is ∠AFP=∠BGM.

Because PE∨BC

So ∠ AFP =∠GMB.

So let ∠AFP=∠BGM.

You need to make ∠GMB=∠BGM.

That is BG=BM= 1.

Let AP=x and Pb = 3-X.

Because AM/BM=AP/PF

So PF=x/3

EG=EF=2-x/3

EB=EG+BG=3-x/3

According to Pythagorean theorem

(3-x)^2+2^2=(3-x/3)^2

The solution is x=3/2.

Make △EFG an equilateral triangle

You need to make ∠ EFG = 60.

Because ∠ EFG = ∠ EGF = ∠ GMB ≠ 60.

Nothing makes a triangle an equilateral triangle.