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In rectangle A, the ratio of the length to the width is 3: 1
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07 Aug 2020, 09:21
07 Aug 2020, 09:21
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Question Stats:
66% (02:27) correct
33% (02:42) wrong based on 105 sessions
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In rectangle A, the ratio of the length to the width is 3: 1. In rectangle B, the ratio of the length to the width is 4: 1. The area of rectangle A is 27 percent of the area of rectangle B. The perimeter of rectangle A is v percent of the perimeter of rectangle B.
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
Kudos for the right solution and explanation
Quantity A |
Quantity B |
\(v\) |
\(54\) |
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
Kudos for the right solution and explanation
Re: In rectangle A, the ratio of the length to the width is 3: 1
[#permalink]
08 Aug 2020, 07:08
08 Aug 2020, 07:08
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A:
area = 3x * 1x =3x^2
perimeter = 2(3x + x) = 8x
B:
area = 4y * y = 4y^2
perimeter = 2(4y + y) = 10y
to find x/y:
area of B * 0.27 = area of A
4y^2 * 0.27 = 3x^2
x/y = 3/5
to find v:
perimeter of B * v/100 = perimeter of A
10y * v/100 = 8x
v = 80 * (x/y)
v = 48.
area = 3x * 1x =3x^2
perimeter = 2(3x + x) = 8x
B:
area = 4y * y = 4y^2
perimeter = 2(4y + y) = 10y
to find x/y:
area of B * 0.27 = area of A
4y^2 * 0.27 = 3x^2
x/y = 3/5
to find v:
perimeter of B * v/100 = perimeter of A
10y * v/100 = 8x
v = 80 * (x/y)
v = 48.
General Discussion
Re: In rectangle A, the ratio of the length to the width is 3: 1
[#permalink]
08 Aug 2020, 03:47
08 Aug 2020, 03:47
2
Consider the sides of Rectangle A as 3x and 1x, then area is 3x² and perimeter is 4x
sides of Rectangle B as 4y and 1y, then area is 4y² and perimeter is 5x
1) => 3x²= (27/100)* 4y²
2) => 4x = (v/100) *5y
From statement 1
x=(3/5)y
substitute x value in statement 2
4 *(3/5)y= (v/100)*5y
v=48
Hence the answer is B
sides of Rectangle B as 4y and 1y, then area is 4y² and perimeter is 5x
1) => 3x²= (27/100)* 4y²
2) => 4x = (v/100) *5y
From statement 1
x=(3/5)y
substitute x value in statement 2
4 *(3/5)y= (v/100)*5y
v=48
Hence the answer is B
