Question

13. If the areas of the adjacent faces of a cuboid are in
the ratio 3 : 4 : 6 and its volume i
3000 ems, then length of the longer side is:
(a) 15 cm
(b) 20 cm
(c) 10 cm
(d) 25 cm

​

Answer 1

Answer:

Let the edge of the cuboid be acm,bcm and ccm.

And, a<b<c

The areas of the three adjacent faces are in ratio 2:3:4

So,

ab:ca:bc=2:3:4 and its volume is 9000cm

3

We have to find the shortest edge of the cuboid

Since,

bc

ab

=

4

2

c

a

=

2

1

∴ c=2a

Similarly,

bc

ca

=

4

3

b

a

=

4

3

∴ b=

3

4a

Volume of cuboid,

V=abc

⇒ 9000=a(

3

4a

)(2a)

⇒ 27000=8a

3

⇒ a

3

=

8

27×1000

⇒ a=

2

3×10

∴ a=15cm

Now, b=

3

4a

=

3

4×15

=20

c=2a=2×15=30cm

∴ The length of the shortest edge is 15cm.

Step-by-step explanation:

hope it helps you...