The surface area of a cuboid is 1372 $c m^{2}$ . If its dimensions (l:b:h) are in the ratio 4 : 2 : 1, then its length(in cm) is:

$14 c m$

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$28 c m$

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$21 c m$

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$24 c m$

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Solution

The correct option is B
$28 c m$

Surface Area = 1372 $c m^{2}$ (Given)

Let length, breadth and height be $l, b$ and $h$ respectively

$\Rightarrow 2 (l \times b + b \times h + l \times h) = 1372$

Since, it is given that

l:b:h = 4:2:1

Let l=4k, b=2k and h=k

$∴ 2 (4 k \times 2 k + 2 k \times k + 4 k \times k) = 1372$

$28 k^{2} = 1372$

$k^{2} = 49 \Rightarrow k = 7$

$∴ l = 4 k = 4 \times 7 = 28 c m$

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