Question

如图,四边形ABCD是长方形,BC=15厘米,CD=8厘米,三角形ABF的面积比三角形DEF大15平方厘米,求DE的长.

Answer 1

设DE=x cm,DF=y cm,则：

AF=AD-DF=15-y,AB=CD=8,

DE/DF=AB/AF,即：x/y=8/(15-y),

S△DEF=1/2*DE*DF=xy/2,

S△ABF=1/2*AB*AF=4(15-y),

S△ABF-S△DEF=4(15-y)-xy/2=15,

解得：x=6(cm),y=90/14(cm),

即DE长为6cm.