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

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Math Expert
Joined: 02 Sep 2009
Posts: 64243
If the perimeter of a square and a rectangle is equal to one another,  [#permalink]

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27 May 2016, 08:03
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25% (medium)

Question Stats:

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

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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

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Joined: 02 Aug 2009
Posts: 8606
Re: If the perimeter of a square and a rectangle is equal to one another,  [#permalink]

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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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Joined: 18 Jan 2010
Posts: 236
Re: If the perimeter of a square and a rectangle is equal to one another,  [#permalink]

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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

Director
Joined: 05 Mar 2015
Posts: 936
Re: If the perimeter of a square and a rectangle is equal to one another,  [#permalink]

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