Question

The perimeter of a rectangular is 240cm, if the length is decreased by 10% and the breadth
is increased by 20%, the perimeter remains unchanged, find the length and breadth of the
rectangle?

Answer 1

Let the dimensions of the

rectangle are

i) length = x cm

breadth = y cm

Perimeter = 240 cm ( given )

2( x + y ) = 240

x + y = 120 ----( 1 )

If length is decreased by 10% and

breadth is increased by 20% then

the new dimensions are

Length = x ( 100-10)/100

= 90x /100

= 9x /10

Breadth = y x ( 100 +20 )/100

= 120y /100

= 12y /10

Perimeter = 240 cm

2 [ 9x /10 + 12y /10 ] = 240

9x + 12y = 1200

Divide each term with 3

3x + 4y = 400-----( 2 )

Multiply equation ( 1 ) with 3 and

Subtract from ( 2 )

y = 40

Put y = 40 in ( 1 )

x = 80

Therefore ,

Required rectangle dimensions are

Length = x = 80 cm

Breadth = y = 40 cm

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Answer 2

Answer:

$\mathfrak{\boxed{\color{violet}{Length\:is\: 80 \:cm\: and \:breadth\: is \:40 \:cm}}}$

Step-by-step explanation:

Given

The perimeter of the rectangle = 240cm

To find

The length and breadth of the rectangle.

When

The breadth is decreased by 10% and length is increased by 20% the perimeter remains unchanged.

As we know,

2×length + 2×breadth = Perimeter

➡️2(length + breadth) = Perimeter

1st equation

2(length +breadth) = 240

➡️length + breadth = 240÷2 = 120

Length decreased by 10% = L - (L × 10/100) = L - L/10 = 10L - L/10 = 9L/10 = 0.9L

Breadth increased 20% = B + (B × 20/100) = B + 2B/10 = 10B + 2B/10 = 12B/10 = 1.2B

2nd Equation

2(0.9L + 1.2B) = 240

➡️0.9L + 1.2B = 240÷2 = 120

Therefore

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

5(0.9L+1.2B)-6(L+B) = 120×5-120×6

➡️4.5L+6B-6L-6B = -120

➡️-1.5L=-120

➡️L = -120÷-1.5 = 80

Breadth = 120 - L = 120 - 80 = 40