Question

the area of a rectangular plot is 528 m².. the length of the plot in metres is 1 more than twice its breadth. Find the length and breath of the plot...

Answer 1

the answer is given in the above picture.
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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  

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

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