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When the lengths of two opposite sides of a square garden

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Areto
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When the lengths of two opposite sides of a square garden [#permalink] New post   27 Jun 2014, 13:16
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When the lengths of two opposite sides of a square garden were increased by x meters each and the lengths of the other two sides were decreased by x meters each, the area of the new garden was 64 square meters. What was the area of the original square garden?

(1) The area of the new garden was 80 percent of the area of the original square garden
(2) x = 4
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Bunuel
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Re: When the lengths of two opposite sides of a square garden [#permalink] New post   27 Jun 2014, 13:56
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When the lengths of two opposite sides of a square garden were increased by x meters each and the lengths of the other two sides were decreased by x meters each, the area of the new garden was 64 square meters. What was the area of the original square garden?

Let the side of the original square be a. We are given that the area of the new garden was (a - x)(a + x) = a^2 - x^2 = 64.

We want to find the area of the original square, so the value of a^2.

(1) The area of the new garden was 80 percent of the area of the original square garden --> 64 = 0.8a^2 --> a^2 = 80. Sufficient.

(2) x = 4 --> a^2 - 4^2 = 64 --> a^2 = 80. Sufficient.

Answer: D.

Hope it's clear.
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Re: When the lengths of two opposite sides of a square garden [#permalink] New post   05 Jul 2014, 23:03
Bunuel - How do we know that the reduced figure is a rectangle. It might even be a parallelogram where the opposite sides of the square are increased in opposite direction and the other opposite sides are reduced in the opposite direction.

Hope I am able to explain the situation :roll:
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Re: When the lengths of two opposite sides of a square garden [#permalink] New post   06 Jul 2014, 02:31
rajmegaurav wrote:
Bunuel - How do we know that the reduced figure is a rectangle. It might even be a parallelogram where the opposite sides of the square are increased in opposite direction and the other opposite sides are reduced in the opposite direction.

Hope I am able to explain the situation :roll:


hi, because each internal angle of the square is 90, therefore the new figure will also have the same internal angle of 90 degrees each, that is why the new figure is rectangle and not a parallelogram.
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Re: When the lengths of two opposite sides of a square garden [#permalink] New post   10 Sep 2017, 23:02
A initial area and y be original side
AreaA y^2
(y+x)(y-x)=64
1) New area is 0.8 of A
64=0.8A
Sufficient

2) x=4

(y+x)(y-x)=64
Then y can be calculated

Therefore sufficient.

D is answer


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Re: When the lengths of two opposite sides of a square garden [#permalink] New post   23 Feb 2021, 19:35
Areto wrote:
When the lengths of two opposite sides of a square garden were increased by x meters each and the lengths of the other two sides were decreased by x meters each, the area of the new garden was 64 square meters. What was the area of the original square garden?

(1) The area of the new garden was 80 percent of the area of the original square garden
(2) x = 4


Original square garden area = A = l * l = ?
we have new square garden area = 64

Sentence -1 The area of the new garden was 80 percent of the area of the original square garden
64 = 80% A
We can get value of A - Sufficient

Sentence -2 x = 4
We already have (l+x) (l-x) = 64
We can get value of l * l - Sufficient

ANS D
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Re: When the lengths of two opposite sides of a square garden [#permalink] New post   26 Jul 2021, 19:38
Let original side be s.
Old area = s*s
New area = (s-x)(s+x) = \(s^2 - x^2\) = 64

(1) The area of the new garden was 80 percent of the area of the original square garden
\(0.8 s^2 = 64\)
We can get Area . Sufficient.

(2) x = 4 . Sufficient.
\(s^2 - 4^2\) = 64
\(s^2 = 80\)

Hence, OA is (D).
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Re: When the lengths of two opposite sides of a square garden [#permalink] New post   13 May 2023, 14:19
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Re: When the lengths of two opposite sides of a square garden [#permalink]
13 May 2023, 14:19
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