Wall and body diagonals

Calculate the lengths of the wall and body diagonals of the cuboid with edge dimensions of 0.5 m, 1 m, and 2 m

Result

u1 =  1.118 m
u2 =  2.062 m
u3 =  2.236 m
d =  2.291 m

Solution:

a=0.5 m b=1 m c=2 m  u1=a2+b2=0.52+12≐1.118≐1.118 ma=0.5 \ \text{m} \ \\ b=1 \ \text{m} \ \\ c=2 \ \text{m} \ \\ \ \\ u_{1}=\sqrt{ a^2+b^2 }=\sqrt{ 0.5^2+1^2 } \doteq 1.118 \doteq 1.118 \ \text{m}
u2=a2+c2=0.52+22≐2.0616≐2.062 mu_{2}=\sqrt{ a^2+c^2 }=\sqrt{ 0.5^2+2^2 } \doteq 2.0616 \doteq 2.062 \ \text{m}
u3=b2+c2=12+22≐5≐2.2361≐2.236 mu_{3}=\sqrt{ b^2+c^2 }=\sqrt{ 1^2+2^2 } \doteq \sqrt{ 5 } \doteq 2.2361 \doteq 2.236 \ \text{m}
d=a2+b2+c2  d=u12+c2=1.1182+22≐2.2913≐2.291 md=\sqrt{ a^2 + b^2 + c^2 } \ \\ \ \\ d=\sqrt{ u_{1}^2 + c^2 }=\sqrt{ 1.118^2 + 2^2 } \doteq 2.2913 \doteq 2.291 \ \text{m}

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