Question

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

Answer 1

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perimeter of rectangle = 240 cm 
Let length of rectangle is L and breadth is B.

perimeter of rectangle = 2(length + breadth) 
240cm = 2(L + B) 

or, 120 = L + B 

L + B = 120 ..........(1) 

And Length is decreased by 10%

So,
New Length = original l - l /10

=> 0.9l

Now,

New Breadth = Original B + 20%

=> B + 20B/100

=> 1.2 B

Therefore,

Perimeter of Rectangle = 2( 0.9l + 1.2B)

=> A.T.Q

ORIGINAL PERIMETER = NEW PERIMETER

=> 240 = 2( 0.9l + 1.2B)

=> 0.9l + 1.2B = 120 --------(2)

From eq1 and 2 we get,

0.9l + 1.2B - ( L + B) = 120 - 120

multiplying 5 with equation (2) - 6 with equation (1)

5(0.9L + 1.2B) - 6(L + B) = 5 × 120 - 6 × 120

4.5 L - 6L = -120

-1.5L = -120

L = 80cm and breadth = 120 - L = 40cm

hence, length of rectangle = 80cm
breadth of rectangle = 40cm
✔✔✔

Answer 2

Let the length of rectangle = l

width = b

perimeter = 2(l+b) = 240

=> l+b = 240/2

=> l + b = 120

=> l = 120 - b

Now, it's given that If it's length is decreased by 10% and it's breadth is increased by 20% we get the same perimeter

new length, after decreasing by 10% = l - 0.1l = 0.9 l
(because 10% of l = 10/100 × l = 0.1 l )

new width, after increasing by 20% = b + 0.2b = 1.2 b
(because 20% of b = 20/100 × b = 0.2b)

New perimeter = 2(0.9l + 1.2b) = 240

=> 0.9l + 1.2b = 240/2

=> 0.9l + 1.2b = 120

Substitute l from above equation,

=> 0.9(120 - b) + 1.2 b = 120

=> 108 - 0.9b + 1.2b = 120

=> 0.3b = 120-108 = 12

=> b = 12/0.3 = 40

l = 120 - 40 = 80

hence, length is 80cm and width is 40cm