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Question
If the areas of the adjacent faces of a rectangular block are in the ratio 2 : 3 : 4 and its volume is 9000 cm3, then the length of the shortest edge is
Options
30 cm
20 cm
15 cm
10 cm
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Solution
Let, the edges of the cuboid be a cm, b cm and c cm.
And, a < b < c
The areas of the three adjacent faces are in the ratio 2 : 3 : 4.
So,
ab : ca : bc = 2 : 3 : 4, and its volume is 9000 cm3
We have to find the shortest edge of the cuboid
Since;
`(ab)/(bc) = 2/4`
`a/c = 1/2`
c = 2a
Similarly,
`(ca)/(bc) = 3/4`
`a/b = 3/4`
`b = (4a)/3`
`b = (4a)/3`
Volume of the cuboid,
V = abc
`9000 = a((4a)/3)(2a)`
27000 = 8a3
a3 =` (27 xx1000)/8`
`a = (3xx10)/2`
a = 15 cm
As` b = (4a)/3 `and c = 2a
Thus, length of the shortest edge is 15 cm .
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