等差数列的三角形的问题。。急啊。。

设公差为d，则a=b-d，c=b+d
a^2+b^2=c^2
(b-d)^2+b^2=(b+d)^2
2b^2-2bd+d^2=b^2+abd+d^2
b^2=4bd
b=4d
所以a=b-d=3d，c=b+d=5d
所以a:b:c=3d:4d:5d=3:4:5

解：Rt△ABC中,∠ACB=90°，三条边a,b,c成等差数列。
设：bc边为b,ac边为c,ab边为c,则依题意有：a-d=b,a+d=c.
(a-d)^2+a^2=(a+d)^2
a^2-2ad+d^2+a^2=a^2+2ad+d^2
2a^2-2ad=a^2+2ad
a^2=4ad
a=4d
当d=1时,有a=4,b=3,c=5,b:a:c=3:4:5
当d=2时,有a=8,b=6,c=10,b:a:c=6:8:10=3:4:5
当d=3时,有a=12,b=9,c=15,b:a:c=9:12:15=3:4:5
.....
当d=n时,有a=4n,b=3n,c=5n,b:a:c=3n:4n:5n=3:4:5
综上所述，三条边的比值是：3：4：5

abc成等差:
a+c=2b => a/c + 1 = 2b/c => a/c = 2b/c - 1

角C=90°:
c²=a²+b² => 1 = (a/c)² + (b/c)²
=> 1 = (2b/c - 1)² + (b/c)²
=> 5(b/c)² -4(b/c) = 0
=> b/c = 0 (舍去) 或 b/c = 4/5

=> a/c = 2b/c - 1 = 3/5

a:b:c=3:4:5

3:4:5