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655-705 (Hard)|   Geometry|      
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Bunuel
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A rectangular public park has an area of 3,600 square feet. It is surr 28 May 2019, 02:32
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55% (hard)

Question Stats:

65% (02:18) correct 35% (02:18) wrong based on 71 sessions

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A rectangular public park has an area of 3,600 square feet. It is surrounded on three sides by a chain link fence. If the entire length of the fence measures 180 feet, how many feet long could the unfenced side of the rectangular park be?

I. 60
II. 90
III. 120

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
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D
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A rectangular public park has an area of 3,600 square feet. It is surr 28 May 2019, 03:14
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Bunuel
A rectangular public park has an area of 3,600 square feet. It is surrounded on three sides by a chain link fence. If the entire length of the fence measures 180 feet, how many feet long could the unfenced side of the rectangular park be?

I. 60
II. 90
III. 120

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
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given
2x+y=180
given in answer option y value
so y=60 x= 60 we get square
and y=120, x= 30
sufficient
IMO E
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A rectangular public park has an area of 3,600 square feet. It is surr 28 May 2019, 19:42
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Bunuel
A rectangular public park has an area of 3,600 square feet. It is surrounded on three sides by a chain link fence. If the entire length of the fence measures 180 feet, how many feet long could the unfenced side of the rectangular park be?

I. 60
II. 90
III. 120

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
Show more

l*b = 3600

Given 2l + b = 180

I. 60
The other value is 60 (3600 = 60*60)
So, 2(60) + 60 = 180. - YES

II. 90
The other value is 40 (3600 = 40*90)
So, 2(90) + 40 = 220 - NO
2(40) + 90 = 170 - NO

III. 120
The other value is 30 (3600 = 120*30)
So, 2(30) + 120 = 180 - YES

IMO Option D

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A rectangular public park has an area of 3,600 square feet. It is surr 01 Jun 2019, 06:24
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Bunuel
A rectangular public park has an area of 3,600 square feet. It is surrounded on three sides by a chain link fence. If the entire length of the fence measures 180 feet, how many feet long could the unfenced side of the rectangular park be?

I. 60
II. 90
III. 120

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
Show more

We have the following equations:

3,600 = WL

Since 3 sides of the fence add to 180, we have:

2L + W = 180

W = 180 - 2L

Substituting, we have:

3,600 = L(180 - 2L)

3,600 = 180L - 2L^2

1,800 = 90L - L^2

L^2 - 90L + 1800 = 0

(L - 60)(L - 30) = 0

L = 60 or L = 30

Thus, we see that if L = 60, then W = 180 - 2(60) = 60, OR if L = 30, then W = 180 - 2(30) = 120.

Since the length of the unfenced side of the park is equal to W, it could be 60 OR 120.

Alternate Solution:

We have the following equations:

3,600 = WL

2L + W = 180

Notice that according to the last equation, the unfenced side is W.

Let’s test each Roman numeral:

Roman numeral I: W = 60

If W = 60, then 2L = 180 - 60 = 120 and thus, L = 60. Since WL = 60 x 60 = 3600, we see that W = 60 is possible.

Roman numeral II: W = 90

If W = 90, then 2L = 180 - 90 = 90 and thus, L = 45. Since WL = 90 x 45 = 4050, we see that W = 90 is not possible.

Roman numeral III: W = 120

If W = 120, then 2L = 180 - 120 = 60 and thus L = 30. Since WL = 120 x 30 = 3600, we see that W = 120 is possible.

Answer: D
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A rectangular public park has an area of 3,600 square feet. It is surr 05 Jun 2019, 05:12
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But , is 60 acceptable here as it will give a square . L =60 and W = 60

And we are taking about the rectangular park .

Are we going by the fact that square is also a rectangle but with equal sides ?
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A rectangular public park has an area of 3,600 square feet. It is surr 12 Apr 2022, 23:30
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