Block or cuboid

The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.

Result

V =  30
S =  62

Solution:

  29=a2+b2 34=b2+c2 13=a2+c2  a2=29b2=2934+c2=2934+13a2 2a2=x2y2+z2  a=2934+132=2  ... b=29+34132=5  ... c=29+34+132=3  V=a b c=2 5 3=30 \ \\ \ \\ 29=a^2+b^2 \ \\ 34=b^2+c^2 \ \\ 13=a^2+c^2 \ \\ \ \\ a^2=29 - b^2=29-34+c^2=29-34+13-a^2 \ \\ 2a^2=x^2-y^2+z^2 \ \\ \ \\ a=\sqrt{ \dfrac{ 29-34+13 }{ 2 } }=2 \ \\ \ \\ ... \ \\ b=\sqrt{ \dfrac{ 29+34-13 }{ 2 } }=5 \ \\ \ \\ ... \ \\ c=\sqrt{ \dfrac{ -29+34+13 }{ 2 } }=3 \ \\ \ \\ V=a \cdot \ b \cdot \ c=2 \cdot \ 5 \cdot \ 3=30
S=2 (a b+b c+c a)=2 (2 5+5 3+3 2)=62S=2 \cdot \ (a \cdot \ b+b \cdot \ c+c \cdot \ a)=2 \cdot \ (2 \cdot \ 5+5 \cdot \ 3+3 \cdot \ 2)=62



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