If the length,breadth and height of a rectang | vedclass

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(D) Let the length,breadth,and height be $6x, 5x,$ and $4x$ meters,respectively.The total surface area of a rectangular parallelopiped is given by the

Vedclass · Accepted Answer

$90, 75, 60$

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(D) Let the length,breadth,and height be $6x, 5x,$ and $4x$ meters,respectively.The total surface area of a rectangular parallelopiped is given by the formula $2(lb + bh + lh) = 33,300$.Substituting the values: $2(6x \cdot 5x + 5x \cdot 4x + 4x \cdot 6x) = 33,300$.$2(30x^{2} + 20x^{2} + 24x^{2}) = 33,300$.$2(74x^{2}) = 33,300$.$148x^{2} = 33,300$.$x^{2} = \frac{33,300}{148} = 225$.$x = \sqrt{225} = 15$.Therefore,the dimensions are:Length $= 6 	imes 15 = 90\, m$.Breadth $= 5 	imes 15 = 75\, m$.Height $= 4 	imes 15 = 60\, m$.

If the length,breadth and height of a rectangular parallelopiped are in the ratio $6:5:4$ and if the total surface area is $33,300\, m^{2}$,then the length,breadth and height of the parallelopiped (in $m$) respectively are:

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