1. Let EM BE perpendicular to AB, EN be perpendicular to BC, and be connected. It is proved.

Triangle CEQ is congruent with triangle BEP, then EP=EQ.

2. The same (1) proves that the triangle ame is similar to the triangle ABC, that is, EM/BC=AE/AC= 1/3, and in the same way, EN/AB= 1/3.

Because AB=BC, EM/EN=EP/EQ= 1/2.

3。 EP/EQ= 1/m, (0<m & lt2+6 square root of lt2+6)

Survey 2

(1) let EQ=X, then s (EPQ) =1/2ep * eq =1/4eq2 = x 2/4. (10 root number 2 < x< 10 root number 3), so when X=EN= 10 root number 2 cm, the minimum value of S(EPQ) is 50 cm2. When X=EF= 10 root number 3, the maximum value is 75 square centimeters.

(2) When x = EB = radical number 10 of 5, S(EPQ)=62. 5, when 50