The dimensions of a cuboid are in the ratio 5:3:1 and its total surface area is 414 m². Find the dimensions ​

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1. Step-by-step explanation:

   GIVEN:-

   =>Dimensions of a cuboid are in the ratio 5:3:1.

   =>Total surface area of cuboid is 414m^2.

   =>Length=5x

   =>Breadth=3x

   =>Height=x

   TO FIND:-

   =>The values of dimensions.

   [tex]\tt\fbox\purple{Understanding The Concept}[/tex]

   According to the question,

   =>We know that the ratios of the dimensions are 5:3:1 and the total surface area is 414m^2.

   =>From this we can find the values of dimensions from the formula of total surface area of cuboid,

   [tex]\bf{ = > 2(lb + bh + hl)}[/tex]

   [tex]\huge\bf\underline{Answer}[/tex]

   Using the given formula,

   [tex]\bf{ 414 =2(5x \times 3x + 3x \times x + 5x \times x) }[/tex]

   [tex]\bf{414 = 2(15x {}^{2} + 3x {}^{2} + 5x {}^{2} )}[/tex]

   [tex]\bf{414 = 2 \times 23x {}^{2} }[/tex]

   [tex]\bf{207 = 23x {}^{2} }[/tex]

   [tex]\bf{x {}^{2} = \dfrac{207}{23} }[/tex]

   [tex]\bf{}x {}^{2} = 9[/tex]

   [tex]\bf{}x = 3[/tex]

   Therefore, the values of dimensions,

   Length= 5x=>15m

   Breadth=3x=>9m

   Height=x=>3

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