Question

Represent the following situation in the form of a quadratic equation:

The area of a rectangular plot is 528 m². The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

Answer 1

Let the breadth of the rectangular plot = x m

Hence, the length of the plot is (2x + 1) m.

Formula of area of rectangle = length × breadth = 528 m²

Putting the value of length and width, we get

(2x + 1) × x = 528

⇒ 2x² + x = 528

⇒ 2x² + x - 528 = 0

⇒ 2x² + 33x - 32x - 528 = 0

⇒ x(2x + 33) - 16(2x + 33) = 0

⇒ (2x + 33)(x - 16) = 0

⇒ 2x + 33 = 0 and x - 16 = 0

⇒ 2x = -33 and x = 16

⇒ x = `(-33)/2` and x = 16

Since,

Width of rectangular plot = x m = 16 m

Length of rectangular plot = 2x + 1 m

= 2 × 16 + 1 m

= 32 + 1 m

= 33 m