Question

If the areas of the adjacent faces of a rectangular block are in the ratio of 3:2:1 and its volume 9000 cu.cm then the length of the shortest side is

Answer 1

Let's assume that the edges of the rectangular block be x cm,y cm and z cm, where x<y<z.

Given that the areas of the adjacent faces of rectangle are in the ratio 3:2:1 and their volume is 9000.

∴ ㅤxy : zx : yz = 3 : 2: 1

We need to find the length of shortest side of block,

$\sf \implies \dfrac{ \cancel{y}x}{z \cancel{y}} = \dfrac{3}{1}$

$\sf \implies \: \dfrac{x}{z} = \dfrac{3}{1}$

$\sf \implies \: \boxed{ \sf{z\: = \frac{x}{3} }}$

Similarly,

$\sf \implies \: \dfrac{zx}{yz} = \dfrac{2}{1}$

$\sf \implies \: \dfrac{x}{y} = \dfrac{2}{1}$

$\sf \implies \: \boxed{ \sf{y = \dfrac{x}{2} }}$

Now, Volume of cuboid will be,

⇒9000 = x × y × z

⇒ 9000 = x ( x/2) (x/3)

⇒ 9000 = x³/6

⇒x = 11.4cm

Value of z = x/3 = 3.8cm, and the length of shortest size is 3.8cm.

Answer 2

Correct question= If the areas of three adjacent faces of a rectangular block are in the ratio of 2 : 3 : 4 and its volume is 9000 cu.cm; then the length of the shortest side is :

A. 10 cm

B. 15 cm

C. 20 cm

D. 30 cm

Answer: Option B

Solution:-

Let lb = 2x, bh = 3x and lh = 4x

Then,

24x3=(lbh)2=9000×9000⇒x3=375×9000⇒x=150

So, lb = 300, bh = 450, lh = 600 and lbh = 9000

∴h=9000300=30l=9000450=20&b=9000600=15

Hence, shortest side = 15 cm