Question

The perimeter of a rectangle is 240cm. if it's length is increased by 10%and its breath is decreased by 20%, we get the same perimeter. find the length and breadth of the rectangle ​

Answer 1

the length will be x 80cm

and length will be y 40cm

step by step explanation

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

Answer 2

In context of question asked,

We have to determine the value of length and breadth of the rectangle.

As per data,

The perimeter of a rectangle is 240cm. if it's length is increased by 10%and its breath is decreased by 20%, we get the same perimeter.

So, let the length and breadth of the rectangle will be l and b cm.

So, perimeter of the rectangle will be $2(l+b) = 2l+2b \:cm$

As when it's length is increased by 10%and its breath is decreased by 20%

So, the new length will be $(l+10\%\:of\:l) = 1.1l$

New breadth will be $(b-20\%\:of\:b) = 0.8b$

Hence, the new perimeter of the rectangle will be $2(l+b) = 2(1.1l+0.8b) = 2.2l+1.6b$

As we have,

The perimeter of rectangle before and after was same,

So, we will equate both value of perimeter,

So, we will get,

$2l+2b = 2.2l+1.6b\\=>2.2l-2l = 2b-1.6b\\=>0.2l=0.4b\\=>\frac{l}{b} =\frac{0.4}{0.2}\\=>\frac{l}{b} = \frac{2}{1}\\=>l = 2b$

Hence, putting the value of l in term of b in the formula for finding the perimeter,

We will get,

$2(l+b) = 240\\=>2(2b+b) = 240\\=>3b = \frac{240}{2}\\=>b = \frac{120}{3} = 40\:cm$

Hence, value of length will be $=2b = 2 \times 40 = 80\:cm$

Hence, value of length and breadth of the rectangle will be 80 cm and 40 cm respectively.