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A rectangular yard is 20 yards wide and 40 yards long. It is surrounde

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A rectangular yard is 20 yards wide and 40 yards long. It is surrounde  [#permalink]

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New post 21 Aug 2018, 19:52
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A
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C
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E

Difficulty:

  95% (hard)

Question Stats:

45% (03:23) correct 55% (03:22) wrong based on 22 sessions

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A rectangular yard is 20 yards wide and 40 yards long. It is surrounded by a thick hedge that grows on the border of the property, but completely within the boundaries of the yard. If the hedge covers an area of 171 square yards, what is the width of the hedge?

A. 160/120
B. 170/120
C. 180/120
D. 191/120
E. 800/120

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Re: A rectangular yard is 20 yards wide and 40 yards long. It is surrounde  [#permalink]

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New post 21 Aug 2018, 20:24
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Bunuel wrote:
A rectangular yard is 20 yards wide and 40 yards long. It is surrounded by a thick hedge that grows on the border of the property, but completely within the boundaries of the yard. If the hedge covers an area of 171 square yards, what is the width of the hedge?

A. 160/120
B. 170/120
C. 180/120
D. 191/120
E. 800/120


Area of the rectangular yard=20*40=800 sq. yard
Given, area of the hedge=171 sq. yard
So, area of the yard that is not covered with hedge=Area of the rectangular yard-Area of the hedge=800-171=629 sq. yard

let 'w' be the width of the hedge, then length of the uncovered yard, L=40-2w and width of the uncovered yard. W=20-2w
Hence, area of the uncovered yard=L*W=(40-2w)(20-2w)=629
Or, \(4w^2-120w+800=629\)
Or, \(4w^2-120w+171=0\)
On solving, we have w=57/2(Not in option) ,3/2 or180/120

Ans. (C)
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A rectangular yard is 20 yards wide and 40 yards long. It is surrounde  [#permalink]

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New post 21 Aug 2018, 20:37

Solution



Given:
    • A rectangular yard is 20 yards wide and 40 yards long.
    • The yard is surrounded by a thick hedge that grows on the border of the property, but completely within the boundaries of the yard.
    • The hedge covers an area of 171 square yards.

To find:
    • The width of the hedge.

Approach and Working:
    • The area of the whole yard = 40 x 20 = 800
    • The area of the hedge = 171
      o Hence, the area of the yard without the hedge = 800 – 171 = 629

If we assume the width of the hedge to be w, then
    • Length of yard without hedge = 40 – 2w
    • Width of yard without hedge = 20 – 2w
    • Therefore, area of yard without hedge = (40 – 2w) (20 – 2w) = 629
      o Or, (40 – 2w) x (20 – 2w) = 37 x 17 = (40 – 2 x 1.5) x (20 – 2 x 1.5)

Comparing both sides of the equation, we can say w = 1.5 = 180/120

Hence, the correct answer is option C.

Answer: C

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Re: A rectangular yard is 20 yards wide and 40 yards long. It is surrounde  [#permalink]

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New post 22 Aug 2018, 00:03
800 = 171 + (40-x)(20-x)

800 = 171 + 800 -60x +x^2
X = 3.
Width = 3/2


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Re: A rectangular yard is 20 yards wide and 40 yards long. It is surrounde &nbs [#permalink] 22 Aug 2018, 00:03
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