Question

如图,已知梯形ABCD中,AD‖BC,AB⊥BC,AB=4,如图,已知梯形ABCD中,AD∥BC,AB⊥

Answer 1

根据题目的易算性,估计：cot∠C=3/4(4分之3).

⑴过D作DF⊥BC于F,则四边形ABFD是矩形,∴DF=AB=4,BF=AD=5,

又cot∠C=CF/DF=3/4,∴CF=3,BC=8,

过E作EG⊥PC于G,∵PE=CE,∴PG=CG,

则CG/EG=cot∠C=3/4,设EG=4m,则PG=CG=3m,∴BP=8-6m,

又RTΔABP∽RTΔEGP,∴PB/PG=AB/EG,(8-6m)/(3m)=4/(4m),m=5/6,

∴BP=3.

⑵BP=X,则CP=8-X,PG=CG=1/2(8-X),

EG=4/5CE=4/5Y,CG=3/5Y,PG=8-X-3/5Y

同⑵相似得：X/(8-X-3/5Y)=4/(4/5Y),

Y=(40-5X)/(X+3),(2.5