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

Answer 1

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 .