Question

三边均为整厘米数，且最长边为10厘米的三角形有（）个

速度！！

Answer 1

三边均为整厘米数，且最长边为10厘米的三角形有（20）个

Answer 2

主要根据两边之和大于第三边和两边之差小于第三边,且最长边为1来考虑.
(1,10,10),
(2,9,10),(2,10,10),
(3,8,10)(3,9,10)(3,10,10)
(4,7,10)(4,8,10)(4,9,10)(4,10,10)
(5,6,10)(5,7,10)(5,8,10)(5,9,10)(5,10,10)
(6,6,10)(6,7,10)(6,8,10)(6,9,10)(6,10,10)
(7,7,10)(7,8,10)(7,9,10)(7,10,10)
(8,8,10)(8,9,10)(8,10,10)
(9,9,10)(9,10,10)
(10,10,10)
1+2+3+4+5+5+4+3+2+1=5*5+5,共30个
如果最长边为11,则为6*6=36个

Answer 3

根据a+b>c的原则共有
(1,11,11)
(2,11,11)(2,10,11)
(3,11,11)(3,10,11)(3,9,11)
(4,11,11)(4,10,11)(4,9,11)(4,8,11)
(5,11,11)(5,10,11)(5,9,11)(5,8,11)(5,7,11)
(6,11,11)(6,10,11)(6,9,11)(6,8,11)(6,7,11)(6,6,11)
(7,11,11)(7,10,11)(7,9,11)(7,8,11)(7,7,11)
(8,11,11)(8,10,11)(8,19,11)(8,8,11)
(9,11,11)(9,10,11)(9,9,11)
(10,11,11)(10,10,11)
(11,11,11)
共36个

Answer 4

20 个：
10,1,10
10,2,9
10,2,10
10,3,8
10,3,9
10,3,10
10,4,7
10,4,8
10,4,9
10,4,10
10,5,6
10,5,7
10,5,8
10,5,9
10,5,10
10,6,6
10,6,7
10,6,8
10,6,9
10,6,10

Answer 5

(1,10,10),(2,9,10),(2,10,10),(3,8,10)(3,9,10)(3,10,10)(4,7,10)(4,8,10)(4,9,10)(4,10,10)
(5,6,10)(5,7,10)(5,8,10)(5,9,10)(5,10,10)(6,6,10)(6,7,10)(6,8,10)(6,9,10)(6,10,10)(7,7,10)
(7,8,10)(7,9,10)(7,10,10)(8,8,10)(8,9,10)(8,10,10)(9,9,10)(9,10,10)(10,10,10)
共30个