Question

The area of the rectangle gets reduced by 80 sq unit if its length reduced by 5 and breadth increased by 2 if its length increased by 10 and its breadth decreased by 5 and area increased by 50 sq unit . find length and breadth

Answer 1

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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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