∠C=90°,AC=8,BC=6
==>AC=10
PM=0.6x,AM=0.8x
PN=AC-AM=8-0.8x
BN=BC-PM=6-0.6x
(1)矩形PMCN的周长=2MP+2PN
=16-0.4x
==>矩形PMCN的周长是14=16-0.4x
==>x=5
(2)S△PAM=0.24x^2
S△PBN=0.24x^2-4.8x+24
S矩形PMCN =2.4x-0.24x^2
假设：S△PAM=S矩形PMCN
==>0.24x^2=2.4x-0.24x^2
==>x=5
S△PAM=S矩形PMCN=6
将x=5代入S△PBN中：
S△PBN=0.24x^2-4.8x+24
=6
==>S△PAM=S矩形PMCN=S△PBN
存在x=5,使得三角形PAM的面积,三角形PBN的面积与矩形PMCN的面积同时相等