Question

The area of a rectangular plot is 528 m 2 . The length of the plot (in meters) is one more than twice its breadth. find the length and breadth of the plot. Advertisement

Answer 1

Given, length of plot ( in meters ) is one more than twice its breadth.

Let the breadth of the plot be x m and length of the plot be ( 2x + 1 ) m .

Given, area of the rectangular plot = 528 m^2

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Area of rectangular shaped 2 D figure = length*breadth

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x( 2x + 1 ) m^2 = 528 m^2

2x^2 + x = 528      [ m^2 cancelled ]

2x^2 + x - 528 = 0

2x^2 + ( 33 - 32 )x - 528 = 0

2x^2 + 33x - 32x - 528 = 0

2x^2 - 32x + 33x - 528 = 0

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

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

x = 16 or x = - 33 / 2

As x is assumed as breadth of the rectangular plot, breadth can't be negative. Therefore value of x is 16

Then,

Breadth of the rectangular plot = x m = 16 m

Length of the rectangular plot = ( 2x + 1 ) m

                                                  = {2( 16 ) + 1 } m

                                                   = 33 m

Length of the rectangular plot  = 33 m

Answer 2

Let the breadth of the plot = 'x' m.

Given that length of the plot is one more than twice its breadth.

Then the length of the plot = 2x + 1.

Now,

Area of the rectangular plot = 528 m^2.

We know that Area of rectangular plot = length * breadth.

⇒ x * (2x + 1) = 528

⇒ 2x^2 + x = 528

⇒ 2x^2 + x - 528 = 0

⇒ 2x^2 + 33x - 32x - 528 = 0

⇒ x(2x + 33) - 16(2x + 33) = 0

⇒ (2x + 33)(x - 16) = 0

⇒ x = -33/2, 16.{Breadth cannot be negative}

⇒ x = 16.

Therefore:

⇒ Breadth of the rectangular plot = 16 m.

⇒ Length of the rectangular plot = 33 m.

Hope it helps!