1已知三角形的三条边为a.b.c,三边上对应高为ha.hb.hc.且a:b:c=2:3:4求ha:hb:hc.越快越好
问题描述:
1已知三角形的三条边为a.b.c,三边上对应高为ha.hb.hc.且a:b:c=2:3:4求ha:hb:hc.越快越好
答
a:b:c=2:3:4,设a=2x,b=3x,c=4x.
设三角形面积为S.
则aha=bhb=chc=2S,
ha=2S/a,hb=2S/b,hc=2S/c,
ha:hb:hc=2S/a:2S/b:2S/c=1/a:1/b:1/c
=1/2x:1/3x:1/4x=1/2:1/3:1/4=6:4:3.