设长方体的长,宽,高分别为a,b,c.对角线为d.
2(ab+bc+ca)=24.(1)
4(a+b+c)=24,
a+b+c=6.(2)
(2)平方-(1),得a^2+b^2+c^2=12,
d^2=a^2+b^2+c^2=12,
d=2√3.