a^2+b^2+c^2+338=10a+24b+26c
a^2-10a+b^2-24b+c^2-26c+338=0
a^2-10a+b^2-24b+c^2-26c+(25+144+169)=0
a^2-10a+25+b^2-24b+144+c^2-26c+169=0
(a-5)^2+(b-12)^2+(c-13)^2=0
(a-5)^2≥0,(b-12)^2≥0,(c-13)^2≥0
a-5=0,b-12=0,c-13=0
a=5,b=12,c=13
5^2+12^2=13^2
所以三角形為∠C=90°的直角三角形