Question

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



pls give the anwer fast

Answer 1

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

Therefore Originally Area = xy sq units.

According to situation 1

Length = x - 5

Breadth = y + 2

New Area = (x - 5) (y +2) which is 80 sq units less than the original area

∴ (x - 5) (y + 2) = xy - 80

xy + 2x - 5y -10 = xy - 80

2x - 5y = - 70 -----( i )

According to situation 2

Length = x + 10

Breadth = y - 5

New Area = (x + 10) (y - 5) which is 50 sq units more than the original area

∴ (x + 10) (y - 5) = xy + 50

xy - 5x + 10y -50 = xy + 50

-5x + 10y = 100 ---( ii )

Multiplying eq (i) with 2 to make coefficient of y equal

4x - 10y = -140 ---- ( iii )

Adding eq (ii) and (iii)

-5x + 10 y + 4x - 10y = 100 - 140

- x =  -40

x = 40

Putting value of x in eq (i)

2(40) - 5y = -70

80 - 5y = -70

-5y = -150

y = 30

∴ Length of the rectangle is 40 units and breadth is 30 units.

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

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