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 will increase by 50 sq units. Find the length and breadth of the rectangle.

Answer 1

Hi ,

Let length of the rectangle = l units

breadth of the rectangle = b units

Area of rectangle = lb

Given ,

the area of a rectangle gets reduced

by 80 sq.units if it's length is reduced

by 5 units and breadth is increased

by 2 units

( l - 5 )( b + 2 ) = lb - 80

=> lb + 2l - 5b - 10 = lb - 80

=> 2l - 5b = - 70 -------( 1 )

Also ,if we increase the length by 10

units and decrease the breadth by 5

units , the area will increase by 50 sq units

( l + 10 )( b - 5 ) = lb + 50

=> lb - 5l + 10b - 50 = lb + 50

=> -5l + 10b = 100 -----( 2 )

solving ( 1 ) and ( 2 ) , we get

l = 40 and b = 30

Therefore ,

Length of the rectangle = l = 40 units

breadth of the rectangle = b = 30 units

I hope this 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

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