Question

The area of a rectangle gets reduced by 80 sq units if its length is reduced by 5 units and breadth is increased by 2 units . if we increase the length by 10 units and decrease the breadth by 5 units the area increased by 50 sq units . Find the length and breadth of the rectangle

Answer 1

sorry coz answer is made too compact but hope you understood , if you have any trouble then comment

Answer 2

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length = 40 units and breadth = 30 units


$\bf{QUESTION}$
The area of a rectangle gets reduced by 80 sq units if its length is reduced by 5 units and breadth is increased by 2 units . if we increase the length by 10 units and decrease the breadth by 5 units the area increased by 50 sq units . Find the length and breadth of the rectangle


$\bf{step \: by \: step \: explanation}$


Let the length and breadth of rectangle be x and y respectively


•°• Area = xy


•°• (x - 5) (y + 2) = xy - 80


i.e, 2x - 5y + 70 = 0______( 1 )


and (x + 10) (y - 5) - xy = 50


==> 5x + 10y = 100

Divide both side by 5

==> x + 2y = 20

==> x - 2y +20 = 0________( 2 )



multiply ( 2 ) by 2 , we get

2x - 4y = -40______( 3 )


subtracting ( 3 ) from ( 1 ), we get

==> -y = -30


$\bf{ \implies \: y = 30 \: }$



•°• 2x -5(30) = -70


==> 2x = -70 + 150


$\bf{ \implies \: x = \frac{80}{2} }$

$\bf \: { \implies \: 40}$


•°• Length = 40 units


and

Breadth = 30 units


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