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The ratio of the areas of a rectangular block's adjacent faces is 2: 3: 4, and the block's volume is 9000 cubic cm.

What is the length of the shortest edge?

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30 cm

20 cm

15 cm

10 cm

answer is C.

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Detailed Solution

The given ratio is

A 1 : A 2 : A 3 = 2 : 3 : 4

.
Since they are adjacent faces, then

(l ⋅ b) : (b ⋅ h) : (h ⋅ l) = 2 : 3 : 4

.
Let’s assume that

x

is the common ratio, then,

⇒ l ⋅ b = 2 x

……(1)

⇒ b ⋅ h = 3 x

……(2)

⇒ l . h = 4 x

……(3)
Divide (1) by (2),

⇒ l b b h = 2 x 3 x ⇒ l h = 23 ⇒ 3 l = 2 h ⇒ h = 32 l

Now, divide (2), by (3),

⇒ b h l h = 3 x 4 x ⇒ b = 34 l

We know that,
Volume of cuboid

= l × b × h

⇒ V = l × 34 l × 32 l ⇒ 9000 = 98 l 3 ⇒ 8000 = l 3 ⇒ l = 20 c m

Now, the breadth b is given by,

b = 34 l ⇒ b = 34 (20) ⇒ b = 15 c m

Now, the height is given by,

h = 32 l ⇒ h = 32 (20) ⇒ h = 30 c m

On comparing 30 > 20 > 15.
So, the shortest edge is the length which is 15 cm.
Hence, option 3 is the correct option.

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