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Re: In rectangle A, the ratio of the length to the width is 3: 1 [#permalink]
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]
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]
3
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]
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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Re: In rectangle A, the ratio of the length to the width is 3: 1 [#permalink]
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