Question

Area of a rectangular plot is 528 m square the length of the plot is 1 m more than twice its breadth find the length and breadth of the plot.

Answer 1

QUESTION

Area of a rectangular plot is 528 m square the length of the plot is 1 m more than twice its breadth find the length and breadth of the plot.


ANSWER


GIVEN

Area of a rectangular plot =528 m square

Length of the plot is 1 m more than twice its breadth.

so , according to given condition

.
Let breathe of rectangular plot=x

so , length. of rectangular plot =(2x+1)



FIND

length and breadth




BACK ON QUESTION




FORMULA USED

$area \: of \: \: rectangular \: plot = l \times b$

so put its value


$x \times (2x + 1) = 528$



$=2 {x}^{2} + x = 528$




$= 2 {x}^{2} + x - 528 = 0$



on solving this quadratic equations we get



$= 2 {x}^{2} + 33x - 32x - 528$



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



$= (x - 16) \: \: and \:( 2x + 33)$




so, x=16 and X=-33/2


NOTE

length can never be negative value .

=> x=16m

so , Breadth=16m

=>
length. of rectangular plot =(2x+1)

=2(16)+1

=32+1

=33m

Answer 2

$\rule{300}3$

$\Huge{\red{\underline{\textsf{Answer}}}}$

Let breadth of a plot is x m.

• According to the question,

$\leadsto$Length of plot = ( 2 × breadth ) + l

$\leadsto$( 2 × x × l ) = ( 2x + 1 ) m.

$\leadsto$Area of reactangular plot = l × b

$\leadsto$( 2x + 1 ) × x = ( 2x² + x ) sq.m.

$\rule{300}3$

• Given: area of plot = 528 sq.m.

$\leadsto$2x² + x = 528

$\leadsto$2x² + x - 528 = 0

$\rule{300}3$

• Required quadratic equation :–

$\mapsto$2x² + x - 528 = 0

$\mapsto$2x² + 33x - 32x - 528 = 0

$\mapsto$x( 2x + 33 ) - 16( 2x + 33 ) = 0

$\mapsto$( 2x + 33 ) ( x - 16 ) = 0

$\mapsto$x - 16 = 0 or 2x + 33 = 0

$\mapsto$x = 16 or x = -33/2 $\large{\pink{\underline{\tt{(Impossible)}}}}$

$\rule{300}3$

Hence, Length of plot is 2x + 1

$\rightarrow$2 × 16 + 1 = $\large{\green{\underline{\tt{ 33m}}}}$

and breadth = $\large{\blue{\underline{\tt{16m}}}}$.

$\rule{300}3$