Question

在三角形ABC中,记三边长为a,b,c.对应边上的高为ha,hb.hc.已知ha:hb:hc=2:x:4

Answer 1

ha:hb:hc=bc:ac:ab=2:x:4

设ha = 2u, hb = xu, hc = 4u

a = 2s/2u = 1/2 v,

b = 2s/xu= 1/x v

c = 2s/4u = 1/4 v

a:b:c = 1/2: 1/x: 1/4

a:b:c = 4x a: 4x b :4x c = 4x *1/2 : 4x *1/x : 4x * 1/4 = 2x : 4 : x