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# The above figure represents a square plot measuring x feet on a side.

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Math Expert
Joined: 02 Sep 2009
Posts: 50627
The above figure represents a square plot measuring x feet on a side.  [#permalink]

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06 Nov 2017, 21:53
00:00

Difficulty:

35% (medium)

Question Stats:

76% (03:02) correct 24% (03:19) wrong based on 27 sessions

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The above figure represents a square plot measuring x feet on a side. The plot consists of a rectangular garden, 48 square feet in area, surrounded by a walk that is 3 feet wide on two opposite sides and 2 feet wide on the other two sides. What is the value of x?

(A) 8
(B) 10
(C) 12
(D) 16
(E) 18

Attachment:

2017-11-07_0941.png [ 925 Bytes | Viewed 629 times ]

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Manager
Joined: 05 Dec 2016
Posts: 244
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: The above figure represents a square plot measuring x feet on a side.  [#permalink]

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07 Nov 2017, 01:43
1
first side of inner rectangle is x-4
second side of inner rectangle is x-6
(x-4)(x-6)=48
solving we get that x = 12
Manager
Joined: 17 May 2016
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Re: The above figure represents a square plot measuring x feet on a side.  [#permalink]

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08 Nov 2017, 12:59
Length of rectangle = x-4
Width = x-6

Area = (x-4)(x-6) = 48
x = 12

Option C is the answer.
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Re: The above figure represents a square plot measuring x feet on a side.  [#permalink]

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08 Nov 2017, 16:42
Bunuel wrote:

The above figure represents a square plot measuring x feet on a side. The plot consists of a rectangular garden, 48 square feet in area, surrounded by a walk that is 3 feet wide on two opposite sides and 2 feet wide on the other two sides. What is the value of x?

(A) 8
(B) 10
(C) 12
(D) 16
(E) 18

Attachment:
2017-11-07_0941.png

Let a and b represent the sides of the rectangular garden. Since the walk is 3 feet wide on two opposite sides and 2 feet wide on the other sides, the sides of the square are a + 6 and b + 4. Since the sides of a square are equal:

a + 6 = b + 4

b = a + 2

Thus, the area of the rectangular garden is ab = a(a + 2) = 48. Let’s solve this for a:

a(a + 2) = 48

a^2 + 2a - 48 = 0

(a - 6)(a + 8) = 0

a = 6 or a = -8

Since the side of a rectangle cannot be negative, we must have a = 6. Thus, the side of the square plot is x = a + 6 = 12.

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Re: The above figure represents a square plot measuring x feet on a side. &nbs [#permalink] 08 Nov 2017, 16:42
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# The above figure represents a square plot measuring x feet on a side.

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