The breadth of a rectangular hall is three-fourth of its length. If the area of the floor is 768 sq. m., then the difference between the length and breadth of the hall is:

The breadth of a rectangular hall is three-fourth of its length. If the area of the floor is 768 sq. m., then the difference between the length and breadth of the hall is:
[A]32 meters
[B]12 meters
[C]8 meters
[D]24 meters

8 meters
Let the length of rectangular hall = x metre
∴ Breadth = \left ( \frac{3}{4}\times x \right )metres
Area of rectangular = Length \times Breadth
= x \times \frac{3}{4}x sq. m. = \frac{3}{4}x^{2}m^{2}
According to the question,
\therefore \frac{3}{4} x^{2} = \frac{768\times 4}{3}
x = \sqrt{\frac{768\times 4}{3}} = 32 m
∴ length = 32 m and Breadth = 24 m
∴ Required difference = 32 – 24 = 8 m
Hence option [C] is the right answer.

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