Question

The perimeter of a rectangle is 240cm. If it's length is decreased by 10% and breadth is increased by 20%, we get the same perimeter. Find the length and the breadth of the both the rectangles​

Answer 1

Answer:

Perimeter of the rectangle given = 240cm

Let x cm be the length of the rectangle,

Let y cm be the breadth of the rectangle,

According to the question:

2(x+y)=240

⇒x+y=120 [First equation]

Now, its length is increased by 10% and its breadth is decreased by 20%

So, the new length be= x+

100

10

x

=

100

100x+10x

=

100

110x

=

10

11x

And the new breadth be = y−

100

20

y

=

100

100y−20y

=

100

80y

=

10

8y

With new length and breadth we get same perimeter.

So,

⇒2(

10

11

x+

10

8

y)=240

⇒

10

11

x+

10

8

y=120

⇒11x+8y=1200 [Second equation]

Now, Second equation −8× [First equation], we get

3x=240

⇒x=80

Putting this value isn First equation,

y=120−80=40

So, length =x=80 cm

and Breadth=y=40 cm