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Perimeter of a rectangle is equal to the perimeter of a square whose d
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28 Jun 2023, 07:08
28 Jun 2023, 07:08
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Perimeter of a rectangle is equal to the perimeter of a square whose diagonal is \(10 \sqrt{2}\). If the length of the rectangle is thrice its breadth, what is the area of the rectangle?
A. 45
B. 75
C. 100
D. 200
E. 225
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
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A. 45
B. 75
C. 100
D. 200
E. 225
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE GEOMETRY
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Re: Perimeter of a rectangle is equal to the perimeter of a square whose d
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05 Jul 2023, 11:46
05 Jul 2023, 11:46
1
Expert Reply
Let's assume the length of the rectangle is L and the breadth is B.
The perimeter of a rectangle is given by the formula: P = 2(L + B).
The perimeter of a square is given by the formula: P = 4s, where s is the side length.
We are given that the perimeter of the rectangle is equal to the perimeter of the square whose diagonal is 10√2. Since the diagonal of a square is √2 times the side length, we can write:
2(L + B) = 4s
L + B = 2s
The diagonal of the square is given as 10√2, so we have:
√(s^2 + s^2) = 10√2
√2s = 10√2
s = 10
Substituting s = 10 into L + B = 2s:
L + B = 2(10)
L + B = 20
We are also given that the length of the rectangle (L) is thrice its breadth (B):
L = 3B
Substituting L = 3B into L + B = 20:
3B + B = 20
4B = 20
B = 5
Now we can find L by substituting B = 5 into L = 3B:
L = 3(5)
L = 15
Therefore, the length of the rectangle is 15 feet and the breadth is 5 feet.
The area of a rectangle is given by the formula: A = L * B.
Substituting the values, we get:
A = 15 * 5
A = 75 square feet
Answer: B
The perimeter of a rectangle is given by the formula: P = 2(L + B).
The perimeter of a square is given by the formula: P = 4s, where s is the side length.
We are given that the perimeter of the rectangle is equal to the perimeter of the square whose diagonal is 10√2. Since the diagonal of a square is √2 times the side length, we can write:
2(L + B) = 4s
L + B = 2s
The diagonal of the square is given as 10√2, so we have:
√(s^2 + s^2) = 10√2
√2s = 10√2
s = 10
Substituting s = 10 into L + B = 2s:
L + B = 2(10)
L + B = 20
We are also given that the length of the rectangle (L) is thrice its breadth (B):
L = 3B
Substituting L = 3B into L + B = 20:
3B + B = 20
4B = 20
B = 5
Now we can find L by substituting B = 5 into L = 3B:
L = 3(5)
L = 15
Therefore, the length of the rectangle is 15 feet and the breadth is 5 feet.
The area of a rectangle is given by the formula: A = L * B.
Substituting the values, we get:
A = 15 * 5
A = 75 square feet
Answer: B
gmatclubot
Re: Perimeter of a rectangle is equal to the perimeter of a square whose d [#permalink]
05 Jul 2023, 11:46
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