Question

Represent the following situations in the form of quadratic equations

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