菱形ABCD的周长为24厘米,角BAC与角ABC之比为2:1,求两条对角线的长及菱形的面积

Question

菱形ABCD的周长为24厘米,角BAC与角ABC之比为2:1,求两条对角线的长及菱形的面积

Answer 1

AB=24/4=6(cm),
设〈ABC=x度,x+2x+2x=180度,x=36度,
以C为圆心,AC长为半径画弧,并AB于E,
则△ECA∽△CBA,
设AC=x,
x/6=(6-x)/x,
x=3√5-3,
AC=3√5-3(cm),
BD/2=√（AB^2-AC^2/4)=(3/2)√(10+2√5),
BD=3√(10+2√5)(cm),
S菱形ABCD=AC*BD/2=(3√5-3)*3√(10+2√5)/2
=9√(10-2√5)(cm)..