Question

The length, breadth and height of a cuboid are in the ratio 4:2:1 and its total surface are is 1372m^2. Find the dimensions of the cuboid.

Please give the answer with steps.

Answer 1

Let The l,b,h be 4x,2x,x repectively
From Total Surface area formula
2(lb+bh+lh)=1372
lb+bh+lh=686
4x*2x+2x*x+4x*x=686
8x² + 2x² + 4x² =686
14x²=686
x²=49
x=√49=7
So Length=4*7=28m
Breath=2*7=14m
and Height=1*7=7m

Answer 2

let the ratio be x
4x:2x:x
TSA OF CUBOID=2(lb+bh+hl)
1372m^2=2(4x×2x+2x×x+x×4x)
1372m^2=2(8x^2+2x^2+4x^2)
1372m^2=2×14x^2
1372m^2=28x^2
x=√1372/28
x=7m

lenght=4x=4×7m=28m
breadth=2x=2×7m=14m
height=x=7m