Question

The Length of a rectangular hall is twice its Breadth and its height is 4m less than its Breadth. The total area of its wall and roof is 864m^2. Determine the dimensions of the hall.

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Answer 1

Let the breadth of the rectangular hall be a m,
So,
Length of the hall = 2a m
Height of the rectangular hall = ( a - 4 ) m.


It is given that the sum of area of its walls and roof is 864 m².

Now,
→ Area of four walls + Area of roof = 864 m²


We know,
Area of four walls = 2( length + breadth ) x height


Now,
= > 2( 2a + a ) x ( a - 4 ) + ( 2a x a ) m² = 864 m²

= > 2( 3a )( a - 4 ) + 2a² = 864

= > 6a( a - 4 ) + 2a² = 864

= > 2{ 3a( a - 4 ) + a² } = 864

= > 3a² - 12a + a² = 432

= > 4a² - 12a - 432 = 0

= > a² - 3a - 108 = 0

= > a² - ( 12 - 9 )a - 108 = 0

= > a² - 12a + 9a - 108 = 0

= > a( a - 12 ) + 9( a - 12 ) = 0

= > ( a - 12 )( a + 9 ) = 0


As the variable 'a' is assumed as the breadth of the rectangular hall, its value can't be negative.
So,
a - 12 = 0
a = 12


Then,
Breadth of the rectangular hall = a m = 12 m
Length of the rectangular hall = 2a m = 2( 12 ) m = 24 m
Height of the rectangular hall = ( a - 4 ) m = ( 12 - 4 ) m = 8 m.


$\texttt{ Breadth of the hall = 12 m}\\\texttt{ Length of the hall = 24 m}\\\texttt{Height of the hall = 8m}$

Answer 2

$\bf\huge\boxed{\boxed{\boxed{Cybary\:Radhe\:Radhe}}}$

■Suppose the breadth of the rectangular hall be a metre.

$\bf\huge\boxed{\boxed{Hence}}}$

Length of hall = 2a metre

Height of rectangular hall = a - 4 metre.

■Sum of area of walls and roof = 864 m².

$\bf\huge\boxed{\boxed{Therefore}}}$

Area of 4 walls + Area of roof

= 864 m²

Area of 4 walls = 2( l + b ) x h

$\bf\huge\boxed{\boxed{Then}}}$

= > 2( 2a + a ) x ( a - 4 ) + ( 2a x a ) m² = 864 m²

= > 2( 3a )( a - 4 ) + 2a² = 864

= > 6a( a - 4 ) + 2a² = 864

= > 2{ 3a( a - 4 ) + a² } = 864

= > 3a² - 12a + a² = 432

= > 4a² - 12a - 432 = 0

= > a² - 3a - 108 = 0

= > a² - ( 12 - 9 )a - 108 = 0

= > a² - 12a + 9a - 108 = 0

= > a( a - 12 ) + 9( a - 12 ) = 0

= > ( a - 12 )( a + 9 ) = 0

=> a + 9 = 0

=> a = -9

=> a - 12 = 0

=> a = 12

■Value can't be negative.

$\bf\huge\boxed{\boxed{a\:=\:12}}}$

●Breadth of rectangular hall = 12 metre

●Length of the rectangular hall = 2a

= 2( 12 ) m = 24 metre

●Height of rectangular hall = ( a - 4 ) metre

= ( 12 - 4 ) metre = 8 metre.

$\bf\huge\boxed{\boxed{\boxed{Radhe\:Radhe}}}$

$\bf\huge\boxed{\boxed{\boxed{Together\:we\:go\:far}}}$