Two rectangles are of same area equal to 480 square cm. They differ in lengths by 6 cm and breadths by 4 cm. What is the difference in their perimeters ?

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CDS 02/2022 Elementary Mathematics Official Paper (Held On 04 Sep 2022)
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  1. 2 cm
  2. 4 cm
  3. 6 cm
  4. 10 cm

Answer (Detailed Solution Below)

Option 2 : 4 cm
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Detailed Solution

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Given:

Two rectangles are of the same area equal = 480 cm2

They differ in length by 6 cm and breadth by 4 cm

Formula used:

Area of rectangle = l × b

Perimeter of rectangle = 2(l + b)

Where, l = length and b = breadth

Shortcut Trick

For the same figure,

The difference in perimeter = Difference in the sum of sides

⇒ P1 - P2 = 2(l + b) - 2(l + 6 + b - 4)

⇒ P1 - P2 = 2(6 - 4) = 4


Alternate Method

Let the length and breadth of two rectangles be l1b1 and l2b2 respectively.

According to the question

⇒ l1b1 = 480         ------(1)

⇒ l2b2 = 480         ------(2)

They differ in length by 6 cm and breadth by 4 cm

Then, length of second rectangle (l2) = (l1 + 6) cm

Then, breadth of second rectangle (b2) = (b1 – 4) cm

Perimeter of first rectangle = 2(l1 + b1

Perimeter of second rectangle = 2(l1 + 6 + b1 – 4)

⇒ 2(l1 + b1) + 4 

The difference in their perimeters is

2(l1 + b1) – 2(l1 + b1) + 4

⇒ 4 cm

∴ The required difference in their perimeters is 4 cm.

Mistake PointsIf the length of the first rectangle increases then to make the area

the same, the breadth will decrease.

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