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(D) The ratio of the sides of the triangle is given as $\frac{1}{4}: \frac{1}{6}: \frac{1}{8}$.To simplify this ratio,we multiply each term by the $LC

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$21$

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(D) The ratio of the sides of the triangle is given as $\frac{1}{4}: \frac{1}{6}: \frac{1}{8}$.To simplify this ratio,we multiply each term by the $LCM$ of $4, 6,$ and $8$,which is $24$.Ratio $= (\frac{1}{4} 	imes 24) : (\frac{1}{6} 	imes 24) : (\frac{1}{8} 	imes 24) = 6: 4: 3$.Let the sides be $6x, 4x,$ and $3x$.The perimeter of the triangle is the sum of its sides,which is $91\, cm$.So,$6x + 4x + 3x = 91$.$13x = 91$.$x = \frac{91}{13} = 7$.The longest side is $6x = 6 	imes 7 = 42\, cm$.The shortest side is $3x = 3 	imes 7 = 21\, cm$.The difference between the longest and shortest side is $42\, cm - 21\, cm = 21\, cm$.

The sides of a triangle are in the ratio $\frac{1}{4}: \frac{1}{6}: \frac{1}{8}$ and its perimeter is $91\, cm$. The difference of the length of the longest side and that of the shortest side is

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