Q. 17

# The area of a rectangular plot is 528 m^{2}. 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.

Answer :

Let the length be l and breadth be b.

Area = l × b

Given Length = 2b + 1

(2b + 1) × b = 528

2b^{2} + b = 528

2b^{2} + b – 528 = 0

2b^{2} + 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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