Question

在矩形ABCD中,AE是角BAC的平分线交BC于E,已知矩形周长80cm,四边形AECD的周长比三角形ABC多20cm,

Answer 1

设AB长x,则BE=AB=x

BD=AC=矩形周长/2-AB=80/2-x=40-x

DE=BD-BE=40-x-x=40-2x

因为四边形AECD的周长-三角形ABC=20cm,所以,

(AC+CD+DE+AE)-(AB+BE+AE)=20

(40-x+x+40-2x+AE)-(x+x+AE)=20

80-4x=20

x=15

40-x=40-15=25

矩形的面积=AB*AC=15*25=375