Question

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

Answer 1

heya friend!!☺☺
here's your answer!!☺☺

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

Then, area of the triangle = xy

Now, from the given conditions we get

( x – 5)(y + 2) = xy – 80

2x – 5y = –70 ...(1)

( x + 10)(y – 5) = xy + 50

5x – 10y = –100 ...(2)

Simplifying (1) and (2), we get

x = 40

putting value of x in (1), we get

y = 30

hence the area of the rectangle,
xy=1200

hope it helps you!!☺☺

Answer 2

$\huge \bf \red{ \mid{ \overline{ \underline{ANSWER}}} \mid}$

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

$\huge \pink{ \mid{ \boxed{ \boxed{ \ulcorner{ \mathbb{THANKS} \ulcorner \mid}}}}}$