Cuboid - edges

The cuboid has dimensions in ratio 4: 3: 5, the shortest edge is 12 cm long. Find:
(A) the lengths of the remaining edges,
(B) the surface of the cuboid,
(C) the volume of the cuboid

Result

a =  16 cm
c =  20 cm
S =  1504 cm2
V =  3840 cm3

Solution:

b=12 k=b/3=12/3=4 a=4⋅ k=4⋅ 4=16 cmb=12 \ \\ k=b/3=12/3=4 \ \\ a=4 \cdot \ k=4 \cdot \ 4=16 \ \text{cm}
c=5⋅ k=5⋅ 4=20 cmc=5 \cdot \ k=5 \cdot \ 4=20 \ \text{cm}
S=2⋅ (a⋅ b+b⋅ c+a⋅ c)=2⋅ (16⋅ 12+12⋅ 20+16⋅ 20)=1504 cm2S=2 \cdot \ (a \cdot \ b+b \cdot \ c+a \cdot \ c)=2 \cdot \ (16 \cdot \ 12+12 \cdot \ 20+16 \cdot \ 20)=1504 \ \text{cm}^2
V=a⋅ b⋅ c=16⋅ 12⋅ 20=3840 cm3V=a \cdot \ b \cdot \ c=16 \cdot \ 12 \cdot \ 20=3840 \ \text{cm}^3

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