The length of a rectangular field is 3 m less than twice its breadth. If the length is decreased by 5 m and the breadth is decreased by 4 m, then the area of the field becomes 800 m². If the breadth of the field is x m, then which quadratic equation represents the given information?

It is given that the breadth of the rectangular field is x m.

The length of the field is 3 m less than twice its breadth.

Thus, length of the field = (2x − 3) m

If the length of the field is decreased by 5 m, then new length = (2x − 3 − 5) m = (2x − 8) m

If the breadth of the field is decreased by 4 m, then new breadth = (x − 4) m

Thus, the area of the field now becomes {(x − 4) (2x − 8)} m² = 800 m²

⇒ 2x² − 8x − 8x + 32 = 800

⇒ 2x² − 16x = 768

⇒ 2x² − 16x − 768 = 0

⇒ x² − 8x − 384 = 0

Hence, the quadratic equation x² − 8x − 384 = 0 represents the given information.