Correct Answer: 1.5

Solution : The total surface area of a rectangular parallelepiped $= 2lw + 2lh + 2wh$
where $l$ is the length, $w$ is the breadth, and $h$ is the height.
Given that the ratio of the length to the breadth is 5 : 3, we can express the length as $5x$ and the breadth as $3x$, where $x$ is a constant.
The height is given as 6 cm.
Substituting these values into the formula,
$⇒558 = 2(5x)(3x) + 2(5x)(6) + 2(3x)(6)$
$⇒558=30x^2+96x$
$⇒5x^2+16x-93=0$
$⇒(x-3)(5x+31)=0$
$⇒x = 3 $
$⇒l = 5x = 15\;\text{cm}$
$\therefore1\;\text{dm}=10\;\text{cm}$
The length in decimeter $=\frac{15}{10}= 1.5\;\text{dm}$
Hence, the correct answer is 1.5.