Question

The length ,breadth and height of a cuboid are in the ratio 4:2:1 and its total surface area is 1372square .find the dimensions of the cuboid?

Answer 1

Answer:

Step-by-step explanation:

Given,

The ratio of length,breadth and height is 4:2:1

Its total surface area is 1372 square cm

Now, lets take the dimensions 4x,2x and 1x

Then, as we all know that the total surface area of a cuboid = 2(lb+bh+hl)

Therefore,

Total surface area of a cuboid= 2(lb+bh+bl)

1372=2{(4x*2x)+(2x*1x)+(4x*1x)}

1372=2(8x^2+2x^2+4x^2)

1372/2=14x^2

196=14x^2

196/14=x^2

14=x^2

√14=x

3.7=x

and therefore the dimensions are

4x= 4*3.7

   =14.8

2x=2*3.7

   =7.4

and x=3.7

Answer 2

let the length be 4x.

let the breadth be 2x.

let the height be x.

TSA of cuboid=2(lb+bh+hl)

1372=2[(4x*2x)+(2x*x)+(4x*x)]

1372=2(8x²+2x²+4x²)

686=14x²

49=x²

x=7

NOW,

l=4x

=4*7

=28cm

b=2x

 =2*7

 =14 cm

h=x

 =7 cm

therefore, the length of the cuboid is 28cm, breadth is 14 cm and height is 7 cm.