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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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.