十八题求解-九游网官方网站入口

设a(0，6m),b(0,0),c(6m,0),d(6m,6m)(m>0).∵be=2ce,∴e(4m,0).∵f为de中点,∴f(5m,3m).
∵等腰rt⊿dfg,设g(p,q)(q>yf=3m),∴(p-4m)² q²=eg²=dg²=(p-6m)² (q-6m)²,
∴0=4mp 12mp-56m²=4m(p 3q-14m),∴p 3q-14m=0,∴p=14m-3q.
∵[(6m)² (2m)²]/4=de²/4=(de/2)²=fg²=(p-5m)² (q-3m)²=[(14m-3q)-5m]² (q-3m)²,
∴0=10(q-3m)²-10m²=10(q-2m)(q-4m),∴q=4m,∴p=14m-3q=14m-3×4m=2m,∴g(2m,4m).
∵(2√5)²=bg²=(2m)² (4m)²,∴0=20m²-20=20(m 1)(m-1),∴m=1.∴d(6,6),f(5,3),g(2,4).
直线bg:y/x=4/2,即y=2x.∵点p′(x,y)在直线bg上(x>xg=2),
∴(6-2)² (6-4)²=dg²=g′d²=(x-6)² (y-6)²=(x-6)² (2x-6)²,∴0=5x²-36x 52=(x-2)(5x-26),
∴x=26/5=5.2,∴y=2x=2×5.2=10.4,∴g′(5.2,10.4).作⊿gfg′的外接矩形,边平行于坐标轴.
∴s⊿gfg′=(5.2-2)(10.4-3)-(5.2-2)(10.4-4)/2-(5.2-5)(10.4-3)/2-(5-2)(4-3)/2=11.2。