The surface area of a cuboid is 1372 cm2. If the ratio length : breadth :

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The surface area of a cuboid is 1372 $c m^{2}$ . If the ratio length : breadth : height is 4:2:1, then its length (in $c m$ ) is

Options:

A . 7

B . 14

C . 21

D . 28

Answer: Option D
:
D

S.A. = 1372 $c m^{2}$ (Given)
$\Rightarrow 2 (l \times b + b \times h + l \times h) = 1372$
$[∵$ Surface area of a cuboid of dimensions $l \times b \times h$ is given by $2 (l b + b h + l h) .]$
Also, it is given that $l : b : h = 4 : 2 : 1$ .
Let $l = 4 k, b = 2 k$ and $h = k$ .
$Then, 2 (4 k \times 2 k + 2 k \times k + 4 k \times k) = 1372$
$⟹ 28 k^{2} = 1372$
$⟹ k^{2} = 49$
$⟹ k = 7$
$∴ l = 4 k = 4 \times 7 = 28 cm$

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