Question

the area of a rectangular plot is 528 m square the length of the plot in metres is 1 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 be x m.
Then, the length of the rectangular plot = (1 + 2x) m.

According to the question,

Length × Breadth = Area
x(1+2x)=528⇒2x2+x−528=0⇒2x2+33x−32x−528=0⇒x(2x+33)−16(2x+33)=0⇒(x−16)(2x+33)=0⇒x−16=0 or 2x+33=0⇒x=16 or x=−332x(1+2x)=528⇒2x2+x-528=0⇒2x2+33x-32x-528=0⇒x(2x+33)-16(2x+33)=0⇒(x-16)(2x+33)=0⇒x-16=0 or 2x+33=0⇒x=16 or x=-332

Since, length and breadth of the rectangle cannot be negative.

Thus, the breadth of the rectangular plot is 16 m.

and the length of the rectangular plot is 1+2×161+2×16 = 33 m.

Answer 2

$\textbf{SOLUTION :}$

Given : Area of the rectangle = 528 m²

Let the breadth of the rectangle be x m

Length of the rectangle = (2x + 1) m

Area of the rectangle = l × b

(2x + 1) x x = 528

2x² + x - 528 = 0

2x² + 33x - 32x - 528 = 0

$\textbf{[By middle term splitting]}$

x(2x + 33) - 16(2x + 33) = 0

(x - 16) (2x + 33) = 0

(x - 16) or (2x + 33) = 0

x = 16 or x = - 33/2

Since, the breadth can't be negative, so x ≠ - 33/2  

Therefore , x = 16

breadth of the rectangle = x =  16 m

Length of the rectangle = 2x + 1 =  (2× 16 + 1) = 32 + 1 = 33 cm  

$\textbf{Hence, the length and the breadth of the plot is 33 cm & 16 cm.}$

$\textbf{HOPE THIS ANSWER WILL HELP YOU…..}$