Question:
The perimeter of a rectangle is 60 cm. If its length is twice its breadth, then its area is:
The perimeter of a rectangle is 60 cm. If its length is twice its breadth, then its area is:
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With sides in a fixed ratio, convert perimeter into a single variable first; then compute the area.
Updated On: Jul 15, 2026
- 200 cm$^2$
- 180 cm$^2$
- 160 cm$^2$
- 220 cm$^2$
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The Correct Option is A
Approach Solution - 1
Let breadth $=b$ cm. Then length $=2b$ cm.
Perimeter $=2(l+b)=2(2b+b)=6b$. Given $6b=60$, so $b=10$ cm and $l=20$ cm.
Area $=l\times b=20\times10=200\ \text{cm}^2$.
Perimeter $=2(l+b)=2(2b+b)=6b$. Given $6b=60$, so $b=10$ cm and $l=20$ cm.
Area $=l\times b=20\times10=200\ \text{cm}^2$.
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Approach Solution -2
The question gives a rectangle with perimeter 60 cm and length equal to twice the breadth, and asks for its area. Rather than solving for the breadth directly, we can test each area option against the given conditions and see which one is consistent.
- 200 cm^2: If the area is 200, and length is twice the breadth, then \( 2b^2 = 200 \), so \( b^2 = 100 \) and \( b = 10 \) cm, giving \( l = 20 \) cm. Checking the perimeter: \( 2(l+b) = 2(20+10) = 60 \) cm, which matches the given perimeter exactly.
- 180 cm^2: Here \( 2b^2 = 180 \), so \( b^2 = 90 \) and \( b \approx 9.49 \) cm, giving \( l \approx 18.97 \) cm. The perimeter would then be about \( 2(18.97+9.49) \approx 56.9 \) cm, which does not equal 60 cm, so this option fails the check.
- 160 cm^2: Here \( 2b^2 = 160 \), so \( b^2 = 80 \) and \( b \approx 8.94 \) cm, giving a perimeter of about \( 2(17.89+8.94) \approx 53.7 \) cm, again not matching 60 cm.
- 220 cm^2: Here \( 2b^2 = 220 \), so \( b^2 = 110 \) and \( b \approx 10.49 \) cm, giving a perimeter of about \( 2(20.98+10.49) \approx 62.9 \) cm, which also does not equal 60 cm.
Only the 200 cm^2 option produces whole number dimensions that satisfy both the 2:1 length to breadth ratio and the given perimeter of 60 cm.
So the correct answer is 200 cm^2.
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Approach Solution -3
Since the perimeter is given, a quick route is to first find the semi-perimeter (half the perimeter, which equals length plus breadth), split that value in the 2:1 ratio given for length to breadth, and then check each area option against the resulting dimensions.
- 200 cm2: Half of the 60 cm perimeter is 30 cm, and splitting 30 in the ratio 2:1 gives a breadth of 10 cm and a length of 20 cm. Multiplying these, \( 20 \times 10 = 200 \) sq cm, which matches this option exactly.
- 180 cm2: For this area to hold with length twice the breadth, the dimensions would need to multiply to 180 while still summing to 30 cm in the 2:1 ratio, but 20 and 10 are the only whole dimensions that split 30 cm in that exact ratio, and they give 200, not 180.
- 160 cm2: The same fixed dimensions of 20 cm and 10 cm are the only ones consistent with the given perimeter and ratio, so an area of 160 cannot arise from them.
- 220 cm2: Likewise, no adjustment to the 20 cm and 10 cm dimensions is possible without breaking either the 60 cm perimeter or the 2:1 length to breadth ratio, so 220 does not fit either.
Splitting the semi-perimeter in the given ratio fixes the dimensions at 20 cm and 10 cm, which multiply to 200 sq cm.
So the correct answer is 200 cm2.
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