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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
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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