Step-by-step explanation:

We know, perimeter of rectangle = 2(length + breadth)

According to the question,

2(length + breadth) = 240

Length + breadth = 240/2

Length + breadth = 120

Length = 120 - breadth ------------------ (1)

New length = length + 10% length

= 110/100 length

New breadth = breadth - 20% breadth

= 80/100 breadth

Since, the perimeter is the same.

2(110/100 length + 80/100 breadth) = 240

1.1 length + 0.8 breadth = 120 --------------- (2)

On solving (1) and (2),

1.1(120 - breadth) + 0.8 breadth = 120

132 - 1.1 breadth + 0.8 breadth = 120

breadth(0.8 - 1.1) = 120 -132

0.3 breadth = 12

Breadth = 12/0.3

Breadth = 40 cm

From (1), length = 120 - 40

Length = 80 cm

Answer:

Let's assume the original length of the rectangle is L cm and the original breadth is B cm.

According to the problem, the perimeter of the rectangle is 240 cm.

Perimeter = 2(L + B) = 240

Dividing both sides of the equation by 2 gives:

L + B = 120

Now, let's consider the second scenario where the length is increased by 10% and the breadth is decreased by 20%.

New length = L + (10/100)L = (110/100)L = 11L/10

New breadth = B - (20/100)B = (80/100)B = 4B/5

Again, the perimeter of the rectangle in this new scenario is:

2((11L/10) + (4B/5)) = 240

Simplifying this equation further gives:

(11L/10) + (4B/5) = 120

To solve this equation, we can multiply both sides by 10 to get rid of the fractions:

11L + 8B = 1200 ----(1)

We now have a system of two equations:

L + B = 120 ----(2)

11L + 8B = 1200 ----(1)

Now, let's solve these equations using the elimination method:

Multiply equation (2) by 8 to make the coefficients of B in both equations equal:

8L + 8B = 960 ----(3)

Now subtract equation (3) from equation (1):

(11L + 8B) - (8L + 8B) = 1200 - 960

3L = 240

L = 80

Substitute the value of L back into equation (2) to find B:

80 + B = 120

B = 120 - 80

B = 40

Therefore, the length of the rectangle is 80 cm and the breadth is 40 cm.

Step-by-step explanation:

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