if the area of three adjacent faces a rectangular block are in..., Area & Volume, General Mathematics

Question:If the area of three adjacent faces of a rectangular block are in the ratio of `2 : 3 : 4` and its volume is `9000 cu ; then the length of the shortest side is :

A `10 cm` 
B `15 cm` 
C `20 cm` 
D `30 cm`

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+ AnswerB

+ ExplanationLet lb`= 2x,` bh`= 3x` and lh`= 4x.`

Then,` 24x^3 = (lbh)^2`

`= 9000 xx 9000`

`:. x^3 = 375 xx 9000`

`or x = 150.`

:. `lb = 300`, 

`bh = 450 & lh = 600 & lbh = 9000.`

`:. h = 9000/300 30,`

`l = 9000/450`

`= 20 & b = 9000/600 = 15.`

:. Shortest side`= 15 cm.`

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