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A rectangular lawn of length 200m by 120m has two roads running along

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A rectangular lawn of length 200m by 120m has two roads running along  [#permalink]

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New post 30 Jul 2015, 11:15
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A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area covered by the two roads?

A. 400
B. 1550
C. 1575
D. 1600
E. 1625

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Re: A rectangular lawn of length 200m by 120m has two roads running along  [#permalink]

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New post 30 Jul 2015, 11:28
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Bunuel wrote:
A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area covered by the two roads?

A. 400
B. 1550
C. 1575
D. 1600
E. 1625


Area Covered by Road Along the Length = 5*200 = 1000 Square Meter

Area Covered by Road Along the Width = 5*120 = 600 Square Meter

Common Area in both Roads (where the roads intersect) = Square with Side 5 meter = 5*5 = 25

Total Area of the Roads = 1000+600-25 = 1575

Answer: option C
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Re: A rectangular lawn of length 200m by 120m has two roads running along  [#permalink]

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New post 30 Jul 2015, 14:34
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Bunuel wrote:
A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area covered by the two roads?


Alternative solution is using estimation...
A. 400 \(< 5 * 200\), which is only one road. Too small
B. 1550 The share space is 25 total, \(5 * 5\), thus 50 is too great of a subtraction
C. 1575 Best answer
D. 1600 = \(5 * 200 + 5 * 120\). Since shared space has not been deducted, too great of area.
E. 1625 > \(5 * 200 + 5 * 120\), thus too big
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Re: A rectangular lawn of length 200m by 120m has two roads running along  [#permalink]

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New post 30 Jul 2015, 15:30
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Bunuel wrote:
A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area covered by the two roads?

A. 400
B. 1550
C. 1575
D. 1600
E. 1625



IMO: C
Attachment:
1.jpg
1.jpg [ 11.62 KiB | Viewed 8434 times ]


Area of the road parallel to the length of the rectangular lawn = 200*5 = 1000 sq m
Area of the road parallel to the breadth of the rectangular lawn = 120*5 = 600 sq m
Area of the intersection of the two perpendicular roads = 5*5 = 25 sq m

Since we calculated the intersection road area twice( once while calculating along length and again while calculating along breadth), we need to subtract from the total sum once to make it even.

Thus area of the paths = 1000+600-25 = 1575 sq m
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Re: A rectangular lawn of length 200m by 120m has two roads running along  [#permalink]

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New post 31 Jul 2015, 02:03
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area of 1st road = (5*120) = 600
area of 2nd road = (5*200) = 1000
area common = (5*5) = 25

thus, net area of roads = 600 + 1000 - 25 = 1575

Ans. = C
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Re: A rectangular lawn of length 200m by 120m has two roads running along  [#permalink]

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New post 31 Jul 2015, 02:09
1
Bunuel wrote:
A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area covered by the two roads?

A. 400
B. 1550
C. 1575
D. 1600
E. 1625



Width of roads=5m
Length of lawn=200 m
Breadth of lawn=120 m
Area of roads= Area of road along length+area of road along breadth-common area
=(200*5)+(120*5)-(5*5)
=1600-25=1575
Answer C
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Re: A rectangular lawn of length 200m by 120m has two roads running along  [#permalink]

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New post 31 Jul 2015, 07:23
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Width of the road running along the length = 5m, so length = 200m. -> Area = 5*200 = 1000 m^2

Width of the road running along the width = 5m, so length = 120m. -> Area = 5*120 = 600 m^2.

Area of intersection = 5*5 = 25 m^2.

Total area covered by the two roads = 1000+600-25 = 1575 m^2. Ans (C).
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Re: A rectangular lawn of length 200m by 120m has two roads running along  [#permalink]

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New post 05 Aug 2015, 23:44
1
Bunuel wrote:
A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area covered by the two roads?

A. 400
B. 1550
C. 1575
D. 1600
E. 1625


Ans: C

solution: two roads running along the center means [ + ] kind of structure.
so we need to reduce the 5*5 box from the total.
so 200*5 + 120*5 - 5*5 = 1575
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Re: A rectangular lawn of length 200m by 120m has two roads running along  [#permalink]

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New post 23 Jan 2018, 13:31
Hi All,

This question is a bit oddly worded, but the 'intent' is to see whether you 'double-count' the overlapping space or not (the part that is covered by BOTH the roads in the 'corner' of the rectangle).

To start, we have a rectangle that is 200m x 120m. There's a 5m wide road that runs the entire length of the rectangle and one that runs the entire width of the rectangle. The areas of the individual roads are...

(5m)(200m) = 1000 m^2
(5m)(120m) = 600 m^2

However, these two roads 'overlap', creating a (5m)(5m) = 25 m^2 space in the corner in which they meet. That space is included in BOTH of those calculations though, so we have to remove one iteration of it. This leaves us with a total 'road area' of...

1000 + 600 - 25 = 1575 m^2

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Re: A rectangular lawn of length 200m by 120m has two roads running along &nbs [#permalink] 23 Jan 2018, 13:31
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