Question

The area of a rectangular plot is 528 m2. the length of the plot is one more than twice it's breadth. find the length and breadth of the plot

Answer 1

Let us take breadth of plot = x m then length will be (1 + 2x) m
ATQ :

Lenght * Breadth = 528
=> (1+2x) * x = 528
=> x + 2x² = 528
=> 2x² + x - 528 = 0
=> 2x² +33x-32x -528 = 0
=> x(2x+33) -16(2x+33) = 0
=> (x-16)(2x-33) = 0

EITHER
x-16=0 => x=16
OR
2x+33= 0 => x= -33/2

Length can't be -ve so x =16

Length = 1+2(16) = 1+32 = 33m
Breadth = 16 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  

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

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