Question

The length Breadth and height of a cuboid are in the ratio 4:2:1 and its total surface area os 1372sqm find the dimensions of the cuboid
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Answer 1

Answer:

The dimension of the cuboid is 28 m: 14 m: 7 m.

Step-by-step explanation:

The total surface area of the cuboid is;

$S=2(lb+bh+hl)$

The ratio of the dimensions are: $l:b:h=4x:2x:x$

Therefore,

$1372 \text{ m}^2=2\times(4x\times2x+2x\times x+4x\times x)\\1372 \text{ m}^2=2\times(8x^2+2x^2+4x^2)\\1372 \text{ m}^2=2\times 14x^2\\1372 \text{ m}^2=28x^2\\49\text {m}^2=x^2\\x=7 \text { m}$

Therefore, the dimension of the cuboid is 28 m: 14 m: 7 m.

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Answer 2

length=4x

breadth=2x

height=x

tsa of cuboid is 2(lb+bh+hl)=1372

2(lb+bh+hl)=1372

lb+bh+hl=1372/2

lb+bh+hl=686

4x*2x+2x*x+x*4x=686

8x^2+2x^2+4x^2=686

14x^2=686

x^2=49

x=7

length=4x=4*7=28m

breadth=2x=2*7=14m

height=x=7m

Step-by-step explanation: