Question

矩形ABCD的面积是5,他的两条对角线交于O1,以AB,AO1为邻边作平行四边形ABC1O1,平行四边形ABC1O1的对

Answer 1

设O1C1交BC于E1,OnCn交BC于En,则

O1E1⊥BC,BE1=BC/2

S平行四边形ABC1O1=AB*BE1=AB*BC/2=5/2

同理BE2=BE1/2=BC/4

S平行四边形ABC2O2=AB*BE2=AB*BC/4=5/4

S平行四边形ABCnOn=AB*BEn=AB*BC/2^n=5/2^n