# 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.