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

(a) 30 cm

(b) 20 cm

(c) 15 cm

(d) 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;

Similarly,

Volume of the cuboid,

As and

Thus, length of the shortest edge is.

Hence; the correct choice is (c).