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The areas of three adjacent faces of a rectangular block are in the ratio of 2: 3: 4 and its volume is $9000 cu . cm,$ find the length of the shortest side.

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answer is C.

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Detailed Solution

It is given that, the volume of the rectangular block is

.
The volume of a cube is expressed as,

V = l b h

, where l, b and h be the length, width and height of a cube.
Suppose the dimensions will of the rectangular block be

l b = 2 x

b h = 3 x

and

h l = 4 x

.
Thus,

V 2 = l b h 2 ⇒ l b ⋅ b h ⋅ h l = 2 x ⋅ 3 x ⋅ 4 x ⇒ l 2 b 2 h 2 = 24 x 3

Therefore,

l b = 2150 ⇒ l b = 300 cm 2

Similarly,

h b = 3150 ⇒ h b = 450 cm 2

And,

h l = 4150 ⇒ h l = 600 cm 2

So, the shortest side is,

l b h 2 = 90002 ⇒ l b h = 9000 ⇒ b 600 = 9000 ⇒ b = 15 cm

Thus, the shortest side is 15cm.
Therefore, option (3) is correct.

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