Question : The ratio of the length and breadth of a rectangular parallelepiped is 5 : 3 and its height is 6 cm. If the total surface area of the parallelepiped is 558 cm². then its length (in dm) is:
Option 1: 9
Option 2: 1.5
Option 3: 10
Option 4: 15

Question

Question : The ratio of the length and breadth of a rectangular parallelepiped is 5 : 3 and its height is 6 cm. If the total surface area of the parallelepiped is 558 cm². then its length (in dm) is:

Option 1: 9

Option 2: 1.5

Option 3: 10

Option 4: 15

Team Careers360 · Accepted Answer

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 $
$⇒l = 5x = 15\; ext{cm}$
$ herefore1\; ext{dm}=10\; ext{cm}$
The length in decimeter $=\frac{15}{10}= 1.5\; ext{dm}$
Hence, the correct answer is 1.5.

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Question : The ratio of the length and breadth of a rectangular parallelepiped is 5 : 3 and its height is 6 cm. If the total surface area of the parallelepiped is 558 cm2. then its length (in dm) is:Option 1: 9Option 2: 1.5Option 3: 10Option 4: 15

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Question : The ratio of the length and breadth of a rectangular parallelepiped is 5 : 3 and its height is 6 cm. If the total surface area of the parallelepiped is 558 cm². then its length (in dm) is:
Option 1: 9
Option 2: 1.5
Option 3: 10
Option 4: 15