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What will be the length and breadth of the rectangle having a perimeter of 240 cm, if its length when increased by 10% and its breadth decreased by 20%, gives the same perimeter?

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80cm, 40cm

80cm, 50cm

70cm, 40cm

90cm, 10cm

answer is A.

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Detailed Solution

We have to find the length and breadth of the rectangle.
For calculating the perimeter of the rectangle:

2 (l + b)

Where,

l

is the length and

b

is the breadth.
Also, perimeter of the rectangle

= 240 cm

Suppose the rectangle's length is

x

cm and

y

cm is the rectangle's width.
As per the question:

2 x + y = 240

⇒ x + y = 2402

⇒ x + y = 120 … .. (1)

And, its length is increased by 10% and its breadth is decreased by 20%.
Then, the new length will be:

x + 10100 x

= 100 x + 10 x 100

= 110 x 100

= 11 x 10

And the unused breadth will be:

y - 20100 y

= 100 y − 20 y 100

= 80 y 100

= 8 y 10

Also, after making the changes, we get the same perimeter.
So,

⇒ 1110 x + 810 y = 120

⇒ 11 x + 8 y 10 = 120

On cross multiplication we get:
11 x+8y=1200….(2)
Multiplying the first equation by 8:
8 x+8y=960….(3)
Now subtracting the second and third equations:
3 x=240

⇒ x = 2403 ⇒ x = 80

Substituting the value of x in (1):
x+y=120

⇒

80+y=120

⇒

y=120-80

⇒

y=40 Thus, it can be concluded that the value for length is 80cm and the breadth of the rectangle will be 40cm.
Therefore, option 1 is correct.

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