the area of three adjacent faces of an rectangular block are in ratio 2:3:4. and it's volume is 9000 cubic cm find the length of shortest side
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Step-by-step explanation:
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
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