Question

长方体AC1中,三条对角线AC=√5,AD1=√10,AB1=√13,则体对角线AC1的长为

Answer 1

(AA1)2+(A1B1)2=(AB1)2

(DD1)2+(AD)2=(AD1)2

(AD)2+(DC)2=(AC)2

AA1=DD1=a

A1B1=DC=b

AD=c

a2+b2=13

a2+c2=10

b2+c2=5

借得 a2=9 b2=4 c2=1

(AC1)2=AC2+a2=14

所以,AC1=根号下14