∵EN⊥AM

∴∠ANE equals ∠ADE equals 90?

∫AE splitting ∠DAM

∴∠NAE equals ∞∠DAE.

AE equals AE

∴△ANE congruence△△△ ade (AAS)

∴AN equals AD and DE equals NE.

∫DE equals NE and EM equals EM.

∴△ENM congruence△△△ ECM (HL)

∴NM equals cm.

∴AM equals AN+NM equals AD+MC.

(2) let MC be equal to X.

∵ABCD is a square.

∴AB equals BC equals AD equals 4.

Then BM is equal to 4-X.

∴ in Rt△ABM:

4? +(4-x)？ Equal to AM?

According to (1), there are:

4? +(4-x)？ Equal to (4+x)?

16+ 16-8x+x？ Equal to 16+8x+x?

Solution: x is equal to 1.

∴AM equals 4+ 1 equals 5.