Cuboid - edges

The sum of all edges cuboid is 8 meters. However, the width is twice shorter as the length, and the height is seven times longer than the width. Determine the dimensions of the cuboid.

Correct answer:

a =  0.8 m
b =  1.6 m
c =  5.6 m

Step-by-step explanation:


a+b+c = 8
a = b/2
c = 7a

a+b+c = 8
a = b/2
c = 7·a

a+b+c = 8
2a-b = 0
7a-c = 0

Pivot: Row 1 ↔ Row 3
7a-c = 0
2a-b = 0
a+b+c = 8

Row 2 - 2/7 · Row 1 → Row 2
7a-c = 0
-b+0.286c = 0
a+b+c = 8

Row 3 - 1/7 · Row 1 → Row 3
7a-c = 0
-b+0.286c = 0
b+1.143c = 8

Row 3 + Row 2 → Row 3
7a-c = 0
-b+0.286c = 0
1.429c = 8


c = 8/1.42857143 = 5.6
b = 0-0.28571428571429c/-1 = 0-0.28571429 · 5.6/-1 = 1.6
a = 0+c/7 = 0+5.6/7 = 0.8

a = 4/5 = 0.8
b = 8/5 = 1.6
c = 28/5 = 5.6

Our linear equations calculator calculates it.



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