Q. 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:
Answer: 8 meters
Notes: Let the length of rectangular hall = x metre
∴ Breadth $latex = \left ( \frac{3}{4}\times x \right )metres&s=1$
Area of rectangular = Length $latex \times$ Breadth
$latex = x \times \frac{3}{4}x sq. m. = \frac{3}{4}x^{2}m^{2}&s=1$
According to the question,
$latex \therefore \frac{3}{4} x^{2} = \frac{768\times 4}{3}&s=1$
$latex x = \sqrt{\frac{768\times 4}{3}} = 32 m&s=1$
∴ length = 32 m and Breadth = 24 m
∴ Required difference = 32 - 24 = 8 m
Hence option [C] is the right answer.
