Q17 of 108 Page 46

The area of a rectangular plot is 528 m2. The length of the plot (in m) is 1 more than double of breadth. Representing by the required quadratic equation find the length and breadth of the plot.

Let the length be l and breadth be b.

Area = l × b


Given Length = 2b + 1


(2b + 1) × b = 528


2b2 + b = 528


2b2 + b – 528 = 0


2b2 + 33b – 32b – 528 = 0


2b(b – 16) + 33(b – 16) = 0


(2b + 33) (b – 16) = 0


Solving the first part,


2b + 33 = 0


2b = -33


b = -33/2


Solving second part,


b – 16 = 0


b = 16


Breadth cannot be negative.


So breadth = 16 m


Length = 2 × 16 + 1


= 33 m


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