The surface area of the cuboid is 1372 sq. cm. If its dimensions are in the ratio of 4: 2: 1. Then find its length.
Given:
The surface area of the cuboid is 1372 sq. cm. Its dimensions are in the ratio of 4: 2: 1.
To do:
We have to find its length.
Solution:
Let the length, breadth and height of the cuboid be $4x, 2x$ and $x$.
Surface area of a cuboid of length $l$, breadth $b$ and height $h$ is $2(lb+bh+lh)$.
Therefore,
$2[(4x)(2x)+(2x)(x)+(4x)(x)]=1372$
$8x^2+2x^2+4x^2=\frac{1372}{2}$
$14x^2=686$
$x^2=\frac{686}{14}$
$x^2=49$
$x=\sqrt{49}$
$x=7\ cm$
$\Rightarrow 4x=4(7)\ cm=28\ cm$
Length of the cuboid is 28 cm.
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