A) 8 m
B) 12 m
C) 24 m
D) 32 m
Correct Answer: A
Solution :
Let the length of rectangular hall \[=x\,m\] \[\therefore \] Breadth \[=\frac{3}{4}\times x\,m\] We know that Area of rectangular = Length \[\times \] Breadth \[=x\times \frac{3}{4}\,sq\,m=\frac{3}{4}{{x}^{2}}{{m}^{2}}\] \[\therefore \] According to question, \[\frac{3}{4}{{x}^{2}}=768\] \[\therefore \] \[{{x}^{2}}=\frac{768\times 4}{3}\] or, \[x=\sqrt{\frac{768\times 4}{3}}=32\,m\] \[\therefore \] Length = 32 cm and Breadth = 24 m \[\therefore \] Required difference \[=32-24=8\,m\]
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