Question

the length breadth and height of a cuboid are in the ratio 5:3:2 . find the dimensions of the cuboid if its surface area is 558 cm sq

Answer 1

Dear Student,

Please find below the solution to the asked query:

Given :  Ratio of length, breadth and height of a cuboid is 5 : 3 : 2 ,  Let ratio coefficient =  x  , So

Length of cuboid  = 5 x  ,

Breadth of cuboid  = 3 x 

And

Height of cuboid  = 2 x 

Also given surface area of cuboid  = 558 cm2, 

We know surface area of cuboid  = 2 ( Length × Breadth + Length × Height + Breadth ×Height ) , Substitute all values we get 

2 ( 5 x × 3 x  + 5 x × 2 x  + 3 x × 2 x  ) =  558

⇒ 2 ( 15 x2  + 10 x2  + 6 x2  ) = 558

⇒ 2 × 31 x2 = 558

⇒ 62 x2 = 558

⇒ x2 = 9

⇒ x2 = 32

⇒ x = 3

Therefore,

Length of cuboid  = 5 × 3 =  15 cm ,

Breadth of cuboid  = 3 × 3  =  9 cm  

And

Height of cuboid  = 2 × 3 = 6 cm 
Hope this information will clear your doubts about topic.

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Answer 2

let ratio = x
5=5x
3=3x
2=2x
5x +2x +3x = 558
10x =558
x =558/10
x =55.8
length = 5x 55.8
=279cm
breadth=3x 55.8
=167.4cm
height = 2x 55.8
=111.6 cm