The length of a rectangular plot is 8 m greater than its breadth. If the area of the plot is 308 m2, find the length of the plot.

Let, the breadth of the rectangular plot be x m. Then the length of rectangular plot = (x + 8) m
∴ Area = Length × Breadth = x(x + 8)m² But the area of the plot is given to be 308 m²
∴ x( x + 8 ) = 308 ⇒ x² + 8x - 308 = 0
⇒ x² + 22x - 14x - 308 = 0
⇒ x( x + 22 ) - 14 ( x - 22 ) = 0
⇒ ( x + 22 ) ( x - 14 ) = 0
⇒ x = 14, -22
But, x = −22 is not possible, since breath cannot be negative
∴ x = 14
Hence the breadth of the rectangular plot = 14 m Length of the rectangular plot = (14 + 8) m = 22 m.