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# If a rectangle with length 8 and width x has the same perimeter as a

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
If a rectangle with length 8 and width x has the same perimeter as a  [#permalink]

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06 Nov 2017, 21:52
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Difficulty:

25% (medium)

Question Stats:

94% (00:40) correct 6% (00:48) wrong based on 30 sessions

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If a rectangle with length 8 and width x has the same perimeter as a square with side of length 6, what is the value of x?

(A) 2
(B) 4
(C) 7
(D) 10
(E) 16

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Re: If a rectangle with length 8 and width x has the same perimeter as a  [#permalink]

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06 Nov 2017, 22:47
Perimeter of square = 4*side = 4*6 = 24
Perimeter of rectangle = 2(length+width) = 2(8+x)

Equate them, 2(8+x) = 24. This gives x=4

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Re: If a rectangle with length 8 and width x has the same perimeter as a  [#permalink]

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08 Nov 2017, 16:45
Bunuel wrote:
If a rectangle with length 8 and width x has the same perimeter as a square with side of length 6, what is the value of x?

(A) 2
(B) 4
(C) 7
(D) 10
(E) 16

Recall that the formula for the perimeter of a rectangle is 2L + 2W. Thus, we can create the following equation:

2(8) + 2x = (4)(6)

16 + 2x = 24

2x = 8

x = 4

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Re: If a rectangle with length 8 and width x has the same perimeter as a  [#permalink]

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08 Nov 2017, 18:28
Bunuel wrote:
If a rectangle with length 8 and width x has the same perimeter as a square with side of length 6, what is the value of x?

(A) 2
(B) 4
(C) 7
(D) 10
(E) 16

Length of rectangle = 8
Width of rectangle = x

Perimeter of rectangle = 2(8+x)

Perimeter of square = 4*6

2*(8+x) = 4*6
8+x = 12
x = 4

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Posts: 7335
Re: If a rectangle with length 8 and width x has the same perimeter as a  [#permalink]

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08 Nov 2017, 18:56
Bunuel wrote:
If a rectangle with length 8 and width x has the same perimeter as a square with side of length 6, what is the value of x?

(A) 2
(B) 4
(C) 7
(D) 10
(E) 16

Hi,
Ofcourse Q has already been answered above in the Correct way, just a fun fact/observation.

The side of square would always be AVERAGE of the two sides of rectangle.

So $$6=\frac{8+x}{2}......12=8+x..........x=4$$
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: If a rectangle with length 8 and width x has the same perimeter as a   [#permalink] 08 Nov 2017, 18:56
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