Correct Answer: 1,600

Explanation:

Let the width of the rectangular field be x meter

Length of the rectangular field is 3x meter

According to the question, 3x$\times$x= 768

=> 3x$^{2}$ = 768

=> x$^{2}$ = $\frac{768}{3}$

=> x$^{2}$ = 256

so, x=16

so, length= 3 X 16 = 48 meter and width = 16 meter

so, Perimeter = 2(48 + 16) = 128 meter

Perimeter of square = Perimeter of rectangular field

so, Perimeter of square = 128 meter

so, Side of square = $\frac{128}{4}$ = 32 meter = 32 X 100 = 3200cm

so, Area of square field = (3200 x 3200) sq.cm.

Area of tiles = (80 X 80) sq.cm.

so, Number of Required tiles = $\frac{3200×3200}{80×80}$ =1,600