Question

area of cuboid is 1792 square CM if the Length breadth and height are in ratio 4 is to 2 is to 1 then find its length

Answer 1

I hope this will help you

Answer 2

Answer:

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Given:

${\sf{Surface \:area \:of \:cuboid = 1792cm^2}}</p><p></p><p>{\sf{Length:Breadth:Height = 4:2:1}}</p><p>$

To find:

Dimensions of cuboid

Solution:

Its given that length:breadth: height = 4:2:1.

Let the length,breadth and height respectively be 4x,2x and x.

$\boxed{\sf{\red{Surface \:Area\: of \:Cuboid = 2(lb+bh+hl)}}}$

Substituting the values of l,b and h....

$1792 = 2[(4x)(2x)+(2x)(x) + (x)(4x) ]\\ 896 = 8 {x}^{2} + 2 {x}^{2} + 4 {x}^{2} \\ 896 = 14 {x}^{2} \\ {x}^{2} = 896 \div 14 \\ {x}^{2} = 64 \\ x = \sqrt{64} </p><p></p><p>\boxed{x = 8}$

Now ,

length = 4x = 4(8) = 32cm

breadth = 2x = 2(8) = 16cm

height = x = 8cm

Therefore,the length, breadth and height of the cuboid is 32cm, 16cm and 8cm respectively.

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