The area of a rectangular plot is 528 m2. Length of a plot (in m) is 1

1.	The area of a rectangular plot is 528 m2. Length of a plot (in m) is 1 more than twice of breadth. By forming quadratic equation, find the length and breadth of the plot.
Answer» Let breadth of a plot is x m. According to question, Length of plot = (2 × breadth) + l = (2 × x + 1) = (2x + 1) m. Area of rectangular plot = l × b = (2x + 1) × x = (2x² + x) sq. m. Given : Area of plot = 528 sq. m. 2x² + x = 528 ⇒ 2x² + x – 528 = 0 Required quadratic equation is : 2x² + x – 528 = 0 ⇒ 2x² + 33x – 32x – 528 = 0 ⇒ x(2x + 33) – 16(2x + 33) = 0 ⇒ (2x + 33) (x – 16) = 0 ⇒ x – 16 = 0 or 2x + 33 = 0 ⇒ x = 16 or x = -33/2 (impossible) Hence, Length of plot is 2x + 1 = 2 × 16 + 1 = 33 m and breadth is 16 m.

The area of a rectangular plot is 528 m2. Length of a plot (in m) is 1 more than twice of breadth. By forming quadratic equation, find the length and breadth of the plot.

Answer»

Let breadth of a plot is x m.

According to question,

Length of plot = (2 × breadth) + l

= (2 × x + 1) = (2x + 1) m.

Area of rectangular plot = l × b

= (2x + 1) × x = (2x² + x) sq. m.

Given : Area of plot = 528 sq. m.

2x² + x = 528

⇒ 2x² + x – 528 = 0

Required quadratic equation is :

2x² + x – 528 = 0

⇒ 2x² + 33x – 32x – 528 = 0

⇒ x(2x + 33) – 16(2x + 33) = 0

⇒ (2x + 33) (x – 16) = 0

⇒ x – 16 = 0 or 2x + 33 = 0

⇒ x = 16 or x = -33/2 (impossible)

Hence, Length of plot is 2x + 1

= 2 × 16 + 1 = 33 m

and breadth is 16 m.