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Area of a rectangle with perimeter 20
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25 May 2026, 10:09
25 May 2026, 10:09
Expert Reply
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Question Stats:
76% (01:29) correct
23% (01:10) wrong based on 17 sessions
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Quantity A |
Quantity B |
Area of a rectangle with perimeter 20 |
Area of a triangle with base 5 and height 10 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Re: Area of a rectangle with perimeter 20
[#permalink]
28 May 2026, 07:25
28 May 2026, 07:25
Expert Reply
Explanation
Analyze Quantity A
We are told the rectangle has perimeter 20.
Let length = \(l\), width = \(w\)
\(2(l+w)=20⇒l+w=10\)
Area of rectangle:
\(A=lw\)
But we only know the sum, not the individual values. So area is not fixed.
If \(l=1,w=9⇒A=9\)
If \(l=5,w=5⇒A=25\) (maximum)
So:
Minimum area → close to 0 (theoretically)
Maximum area → 25
Hence Quantity A is variable.
Analyze Quantity B
Triangle area:
\(\frac{1}{2}*5*10=25\)
So Quantity B = 25 (fixed)
Quantity A can be less than 25, equal to 25, or even less than Quantity B depending on dimensions. It is not uniquely determined relative to 25
Answer: D
Analyze Quantity A
We are told the rectangle has perimeter 20.
Let length = \(l\), width = \(w\)
\(2(l+w)=20⇒l+w=10\)
Area of rectangle:
\(A=lw\)
But we only know the sum, not the individual values. So area is not fixed.
If \(l=1,w=9⇒A=9\)
If \(l=5,w=5⇒A=25\) (maximum)
So:
Minimum area → close to 0 (theoretically)
Maximum area → 25
Hence Quantity A is variable.
Analyze Quantity B
Triangle area:
\(\frac{1}{2}*5*10=25\)
So Quantity B = 25 (fixed)
Quantity A can be less than 25, equal to 25, or even less than Quantity B depending on dimensions. It is not uniquely determined relative to 25
Answer: D
gmatclubot
Re: Area of a rectangle with perimeter 20 [#permalink]
28 May 2026, 07:25
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