Wall and body diagonals

The block/cuboid has dimensions a = 4cm, b = 3cm and c = 12cm. Calculates the length of the wall and body diagonals.

Result

u1 =  5 cm
u2 =  12.369 cm
u3 =  12.649 cm
d =  13 cm

Solution:

a=4 cm b=3 cm c=12 cm  u1=a2+b2=42+32=5 cma=4 \ \text{cm} \ \\ b=3 \ \text{cm} \ \\ c=12 \ \text{cm} \ \\ \ \\ u_{1}=\sqrt{ a^2+b^2 }=\sqrt{ 4^2+3^2 }=5 \ \text{cm}
u2=b2+c2=32+122≐3 17≐12.3693≐12.369 cmu_{2}=\sqrt{ b^2+c^2 }=\sqrt{ 3^2+12^2 } \doteq 3 \ \sqrt{ 17 } \doteq 12.3693 \doteq 12.369 \ \text{cm}
u3=a2+c2=42+122≐4 10≐12.6491≐12.649 cmu_{3}=\sqrt{ a^2+c^2 }=\sqrt{ 4^2+12^2 } \doteq 4 \ \sqrt{ 10 } \doteq 12.6491 \doteq 12.649 \ \text{cm}
d=a2+b2+c2=42+32+122=13 cmd=\sqrt{ a^2+b^2+c^2 }=\sqrt{ 4^2+3^2+12^2 }=13 \ \text{cm}

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