17) The breath of a room is twice its height and half its length. The volume
of the room is 512 m3. The length of the room is

2 thoughts on “17) The breath of a room is twice its height and half its length. The volume<br />of the room is 512 m3. The length of the room is”

1. Given
   =>Volume of the room = 512m^3

   =>breadth (b) of the room = 2* height (h)
   => b = 2h
   => h = 1/2*b

   =>breadth (b) of the room = 1/2 * length (l)
   => b = 1/2*l
   => l = 2*b

   Solution
   Volume of the room = l*b*h

   =>512 = 2b* b * 1/2 b
   =>512 = b* b * b
   =>512 = b^3
   =>b = 8 m

   The length of the room = 2b
   = 2*8
   = 16 m

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2. [tex]{ \underline{ \underline{ \tt{ \huge{Question}}}}} : [/tex]

   • The breath of a room is twice its height and half its length. The volume of the room is 512 m3. The length of the room is

   [tex]{ \underline{ \underline{ \tt{ \huge{To \: \: Find}}}}} : [/tex]

   • Find the length of the room.

   [tex]{ \underline{ \underline{ \tt{ \huge{Given}}}}} : [/tex]

   • The breath of a room is twice its height and half its length. The volume of the room is 512 m³.

   [tex]{ \underline{ \underline{ \tt{ \huge{Solution}}}}} : [/tex]

   • Let the height be ” x ”

   • Breadth is ” 2x “

   • Length is ” 4x “

   • Volume is ” 512 m³ “

   [tex]{ \implies{ \tt{Volume = Length \times Breadth \times Height}}}[/tex]

   [tex]{ \implies{ \tt{512 = 4x \times 2x \times x}}}[/tex]

   [tex]{ \implies{ \tt{512 = { 8x }^{ 3 } }}}[/tex]

   [tex]{ \implies{ \tt{ { x }^{ 3 } = \cancel\dfrac { 512 } { 8 } }}}[/tex]

   [tex]{ \implies{ \tt{ { x }^{ 3 } = 64}}}[/tex]

   [tex]{ \implies{ \tt{a = 2}}}[/tex]

   Hence ,

   • Length is 4x = 16 m

   • Breadth is 2x = 8 m

   • Height is x = 4 m

   Reply