Question:medium

The perimeter of a rectangle is 60 cms. If its length is twice its breadth, then its area is:

Updated On: Jul 15, 2026
  • 200 cm2
  • 180 cm2
  • 160 cm2
  • 220 cm2
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The Correct Option is A

Approach Solution - 1

Step 1: Set up the variables.
Let the breadth be \( b \) cm. Since the length is twice the breadth, the length is \( 2b \) cm.

Step 2: Use the perimeter to find b.
Perimeter of a rectangle is \( 2(l+b) \). \[ 2(2b+b) = 60 \] \[ 6b = 60 \] \[ b = 10 \]

Step 3: Find the length and the area.
Length \( = 2b = 20 \) cm. Area \( = l \times b = 20 \times 10 = 200 \) cm².

Step 4: Final Answer.
The rectangle measures 20 cm by 10 cm, giving an area of 200 cm². \[ \boxed{200 \text{ cm}^2} \]
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Approach Solution -2

Since length and breadth are in the ratio 2:1, the rectangle's perimeter can be thought of as made up of 6 equal "breadth units" in total (2 lengths, each worth 2 units, plus 2 breadths, each worth 1 unit), and dividing the perimeter by that total gives the value of one unit directly.

  1. 200 cm²: The perimeter of 60 cm divided across 6 equal units gives \( 60 \div 6 = 10 \) cm per unit. Since breadth is 1 unit and length is 2 units, breadth is 10 cm and length is 20 cm, giving an area of \( 20 \times 10 = 200 \) cm², which matches.
  2. 180 cm²: Since each unit is fixed at exactly 10 cm by the perimeter division, the dimensions cannot shrink or stretch to produce this smaller area.
  3. 160 cm²: This area would require a smaller unit value than the 10 cm fixed by dividing the perimeter into 6 parts, so it does not fit.
  4. 220 cm²: This area would require a larger unit value than 10 cm, which the perimeter division does not allow.

Splitting the perimeter into 6 equal ratio-based units fixes each unit at 10 cm, giving breadth 10 cm and length 20 cm, and an area of exactly 200 cm².

Therefore, the correct answer is 200 cm².

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