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If the perimeter of a square and a rectangle is equal to one another,

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If the perimeter of a square and a rectangle is equal to one another,  [#permalink]

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New post 27 May 2016, 08:03
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Question Stats:

87% (01:52) correct 13% (02:09) wrong based on 44 sessions

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Re: If the perimeter of a square and a rectangle is equal to one another,  [#permalink]

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New post 27 May 2016, 09:28
Bunuel wrote:
If the perimeter of a square and a rectangle is equal to one another, find out the ratio of the area of both these shapes in case the sides of the rectangle are in the
ratio of 2 :5.

(A) 40 : 49
(B) 24 : 25
(C) 4 : 5
(D) 5 : 6
(E) 4 : 9



Hi,

since perimeter are same and ratio of sides of rectangle is 2:5, the sides are 2x and 5x....
sides of square will be 3.5x and 3.5x.....
area =\(\frac{3.5x*3.5x}{2x*5x} = \frac{3.5*3.5}{10}= \frac{49}{40}\)....
since the ratio of two sides is asked and not in any particular order ans can be 40/49 or 49/40
A
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Re: If the perimeter of a square and a rectangle is equal to one another,  [#permalink]

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New post 27 May 2016, 09:57
Bunuel wrote:
If the perimeter of a square and a rectangle is equal to one another, find out the ratio of the area of both these shapes in case the sides of the rectangle are in the
ratio of 2 :5.

(A) 40 : 49
(B) 24 : 25
(C) 4 : 5
(D) 5 : 6
(E) 4 : 9


Rectangle
Let its sides are 2x and 5x. Perimeter of this rectangle : 2 * (2x+5x) = 14x

Perimeter of Square = 14 x

Side of square: \(\frac{14x}{4}\)

Area of square: \(\frac{7x}{2}\) * \(\frac{7x}{2}\) = 49\(x^2\)/4

Area of rectangle: 2x * 5x = 10 \(x^2\)

Ratio of Rectangle:Square
10 : \(\frac{49}{4}\) or 40: 49

A is the answer.
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Re: If the perimeter of a square and a rectangle is equal to one another,  [#permalink]

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New post 26 Jun 2016, 01:24
Bunuel wrote:
If the perimeter of a square and a rectangle is equal to one another, find out the ratio of the area of both these shapes in case the sides of the rectangle are in the
ratio of 2 :5.

(A) 40 : 49
(B) 24 : 25
(C) 4 : 5
(D) 5 : 6
(E) 4 : 9

Let side of square=a
length of rectangle=l
bredth of rectangle=b
l/b=2/5------->l=2b/5-----(1)
given 4a=2(l+b)-------->4a=2(2b/5+b)
a=7b/10------(2)
we have to find l*b/a^2

substituting from (1) &(2)
(b*2b/5)/49b^2/100------40/49

Ans A
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Re: If the perimeter of a square and a rectangle is equal to one another,   [#permalink] 26 Jun 2016, 01:24

If the perimeter of a square and a rectangle is equal to one another,

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