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In rectangle A, the ratio of the length to the width is 3: 1

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In rectangle A, the ratio of the length to the width is 3: 1 [#permalink] New post   07 Aug 2020, 09:21
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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.

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

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Aaka
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Re: In rectangle A, the ratio of the length to the width is 3: 1 [#permalink] New post   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.
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cvardhan
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Re: In rectangle A, the ratio of the length to the width is 3: 1 [#permalink] New post   08 Aug 2020, 03:47
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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
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Re: In rectangle A, the ratio of the length to the width is 3: 1 [#permalink] New post   08 Aug 2020, 05:26
cvardhan wrote:
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


How did you take perimeter as 4x? Isnt the formula of perimeter of rectangle 2(l+b)?
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Re: In rectangle A, the ratio of the length to the width is 3: 1 [#permalink] New post   12 Aug 2022, 13:38
Aaka wrote:
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.


Sorry for the ignorance, but how does this 4y^2 * 0.27 = 3x^2 become x/y = 3/5?
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Re: In rectangle A, the ratio of the length to the width is 3: 1 [#permalink] New post   14 Aug 2022, 02:29
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BrDickinson wrote:
Aaka wrote:
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.


Sorry for the ignorance, but how does this 4y^2 * 0.27 = 3x^2 become x/y = 3/5?


I hope it is clear till the following step:
A/B = 27/100
This becomes, (3x.x)/(4y.y) = 27/100
which on simplification gives x^2/y^2 = 9/25
As these are sides of a geometrical figure, the lengths cannot be negative. Hence, taking roots on both sides yields x/y=3/5.
Hope it is clear now.
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Re: In rectangle A, the ratio of the length to the width is 3: 1 [#permalink] New post   14 Aug 2022, 04:23
iASindia wrote:
BrDickinson wrote:
Aaka wrote:
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.


Sorry for the ignorance, but how does this 4y^2 * 0.27 = 3x^2 become x/y = 3/5?


I hope it is clear till the following step:
A/B = 27/100
This becomes, (3x.x)/(4y.y) = 27/100
which on simplification gives x^2/y^2 = 9/25
As these are sides of a geometrical figure, the lengths cannot be negative. Hence, taking roots on both sides yields x/y=3/5.
Hope it is clear now.


Super helpful.
Thank you so much!
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abhinavv
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Re: In rectangle A, the ratio of the length to the width is 3: 1 [#permalink] New post   12 Jan 2025, 04:00
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let b area= 100
a area =27
3x^2=27=x=3
a length width = 9,3 perimeter of a=2*12=24
b=100
4y^2=100=y=5
b length width=20,5, perimeter of b=2*25=50
24=v% of 50= v=48
B answer
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Re: In rectangle A, the ratio of the length to the width is 3: 1 [#permalink] New post   18 Jun 2026, 01:04
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Re: In rectangle A, the ratio of the length to the width is 3: 1 [#permalink]
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