Question:
The perimeter of a rectangle is 60 cms. If its length is twice its breadth, then its area is:
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
The correct option is (A): 200 cm2.
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The question gives a rectangle with perimeter 60 cm and length twice its breadth, and asks for its area. Since length and breadth must satisfy both the perimeter equation and the 2:1 ratio at the same time, we can test each option's implied dimensions against these two conditions.
- 200 cm²: An area of 200 cm² fits breadth 10 cm and length 20 cm, since \( 10 \times 20 = 200 \). Checking the ratio, \( 20 = 2 \times 10 \), so length is indeed twice the breadth. Checking the perimeter, \( 2(20+10) = 2(30) = 60 \) cm, which matches the given perimeter exactly.
- 180 cm²: Breadth 9 cm and length 18 cm would give length twice breadth and an area of \( 9 \times 18 = 162 \), not 180, and testing breadth values that do give 180 with a 2:1 ratio produces a perimeter well away from 60 cm.
- 160 cm²: A 2:1 rectangle with this area needs breadth \( \sqrt{80} \) cm, an irrational value whose perimeter does not equal 60 cm, so it fails the perimeter check.
- 220 cm²: A 2:1 rectangle with this area needs breadth \( \sqrt{110} \) cm, which again does not give a perimeter of 60 cm.
Only the breadth 10 cm, length 20 cm pairing satisfies both the perimeter of 60 cm and the 2:1 length to breadth ratio at once, giving an area of 200 cm².
Therefore, the correct answer is 200 cm².
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This question gives a rectangle with perimeter 60 cm and a length that is twice its breadth, and asks for its area. Setting up the relationship algebraically and solving directly, rather than testing each option's numbers, gives the exact dimensions needed to confirm the area.
- 200 cm²: Let the breadth be \( b \) cm, so the length is \( 2b \) cm. The perimeter equation \( 2(2b+b)=60 \) simplifies to \( 6b=60 \), giving \( b=10 \) and length \( 2b=20 \). The area is then \( 20 \times 10 = 200 \) cm², matching this option exactly.
- 180 cm²: Since the algebra above fixes the breadth at exactly 10 cm and length at 20 cm with no other solution possible under the given constraints, an area of 180 cm² cannot arise from this rectangle.
- 160 cm²: This value is also inconsistent with the unique breadth and length pair, 10 cm and 20 cm, that the perimeter and ratio conditions together fix.
- 220 cm²: This is likewise ruled out, since the equation \( 6b=60 \) admits only one solution for the breadth, leaving no room for a larger area than 200 cm².
Solving the perimeter equation directly pins the rectangle's dimensions at 10 cm by 20 cm, which gives an area of exactly 200 cm² and leaves no possibility for any of the other listed values.
Therefore, the correct answer is 200 cm².
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