The length, breadth and height of a rectangular solid are in the ratio of $3: 2: 1$ and its total surface area is $352 \mathrm{~cm}^{2}$, then find its length.
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The length, breadth and height of a rectangular solid are in the ratio of $3: 2: 1$ and its total surface area is $352 \mathrm{~cm}^{2}$, then find its length.

(a) $4 \mathrm{~cm}$

(b) $6 \mathrm{~cm}$

(c) $9 \mathrm{~cm}$

(d) $12 \mathrm{~cm}$
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Solution

According to the question, $l=3 x, b=2 x$ and $h=x$

$\therefore$ Total S.A.

$=2(3 x \times 2 x+2 x \times x+3 x \times x)$

$\Rightarrow 352=2\left(6 x^{2}+2 x^{2}+3 x^{2}\right)$

$\Rightarrow 352=2 \times 11 x^{2}$

$\Rightarrow 352=22 x^{2}$

$\therefore x=\sqrt{\frac{352}{22}}=\sqrt{16}=4 \mathrm{~cm}$

$\therefore l=3 x=3 \times 4=12$

So, the correct option is (D)

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