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# The figure represents the design of a drawbridge that spans a channel

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Math Expert
Joined: 02 Sep 2009
Posts: 48068
The figure represents the design of a drawbridge that spans a channel  [#permalink]

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20 Jan 2015, 07:00
3
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Difficulty:

65% (hard)

Question Stats:

56% (01:37) correct 44% (02:32) wrong based on 106 sessions

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The figure represents the design of a drawbridge that spans a channel 54 meters in width. If the two raisable sections are equal in length and overlap each other by a measure of 2 meters, what will be the clearance width of the bridge in meters, when the sections are raised to an angle of 60 degree ?

A) 25
B) 26
C) 27
D) 28
E) 54

Attachment:

1.png [ 9.08 KiB | Viewed 2500 times ]

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Re: The figure represents the design of a drawbridge that spans a channel  [#permalink]

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20 Jan 2015, 22:01
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The figure represents the design of a drawbridge that spans a channel 54 meters in width. If the two raisable sections are equal in length and overlap each other by a measure of 2 meters, what will be the clearance width of the bridge in meters, when the sections are raised to an angle of 60 degree ?

A) 25
B) 26
C) 27
D) 28
E) 54

Given that raisable sections have an overlap of 2 meters when they cover the channel of 54 meters. Since the raisable sections are of equal length, the length of each section will be 28 metres.. Why (Because consider if there is no overlap and 2 sections are equal in length so to cover the channel each will be 27 meters but since there is overlap of 2 meters so each section will be 28 metres)
Attachment:

1.png [ 12.08 KiB | Viewed 2016 times ]

Now when inclined to 60 degrees, the length of section is 28 metres and we end up with a 30-60-90 degree triangle..So the side opposite 30 degree angle 14 metres

So total clearance will be [m]54-14*2

Ans B =26 meters
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Re: The figure represents the design of a drawbridge that spans a channel  [#permalink]

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22 Jan 2015, 19:09
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Total span = 54 with overlap of 2 meters

Let "x" be the length of each non-overlap section

Then, x + 2 + x = 54

x = 26

Length of each arm = 26+2 = 28

Refer diagram below:

Attachment:

1.png [ 10.52 KiB | Viewed 1951 times ]

When this 28 meters arm is raised 60 degrees, it forms a 30 - 60 - 90 degree right triangle with 28 as its hypotenuse

Sides of 30:60:90 are in ratio $$1: \sqrt{3}:2$$, so the side opposite to 30degree would be 14 (which is the non-cleared section of bridge)

Total clearance = 54 - 2*14 = 26
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The figure represents the design of a drawbridge that spans a channel  [#permalink]

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12 Nov 2016, 00:58
Bunuel wrote:

The figure represents the design of a drawbridge that spans a channel 54 meters in width. If the two raisable sections are equal in length and overlap each other by a measure of 2 meters, what will be the clearance width of the bridge in meters, when the sections are raised to an angle of 60 degree ?

A) 25
B) 26
C) 27
D) 28
E) 54

Attachment:
The attachment 1.png is no longer available

Kudos for a correct solution.

Check solution
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Re: The figure represents the design of a drawbridge that spans a channel  [#permalink]

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11 Sep 2017, 03:40
1
Bunuel wrote:

The figure represents the design of a drawbridge that spans a channel 54 meters in width. If the two raisable sections are equal in length and overlap each other by a measure of 2 meters, what will be the clearance width of the bridge in meters, when the sections are raised to an angle of 60 degree ?

A) 25
B) 26
C) 27
D) 28
E) 54

Attachment:
The attachment 1.png is no longer available

Kudos for a correct solution.

Bunuel => awaiting kudos for correct solution.(mentioning first time though )
Attachments

IMG_4620.JPG [ 1.87 MiB | Viewed 723 times ]

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Re: The figure represents the design of a drawbridge that spans a channel  [#permalink]

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11 Sep 2017, 03:44
sahilvijay wrote:
Bunuel wrote:

The figure represents the design of a drawbridge that spans a channel 54 meters in width. If the two raisable sections are equal in length and overlap each other by a measure of 2 meters, what will be the clearance width of the bridge in meters, when the sections are raised to an angle of 60 degree ?

A) 25
B) 26
C) 27
D) 28
E) 54

Attachment:
1.png

Kudos for a correct solution.

Bunuel => awaiting kudos for correct solution.(mentioning first time though )

This works for 1 week till the OA is revealed.
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Re: The figure represents the design of a drawbridge that spans a channel  [#permalink]

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11 Sep 2017, 03:45
Bunuel wrote:
sahilvijay wrote:
Bunuel wrote:

The figure represents the design of a drawbridge that spans a channel 54 meters in width. If the two raisable sections are equal in length and overlap each other by a measure of 2 meters, what will be the clearance width of the bridge in meters, when the sections are raised to an angle of 60 degree ?

A) 25
B) 26
C) 27
D) 28
E) 54

Attachment:
1.png

Kudos for a correct solution.

Bunuel => awaiting kudos for correct solution.(mentioning first time though )

This works for 1 week till the OA is revealed.

Okay i was not knowing this.
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Re: The figure represents the design of a drawbridge that spans a channel  [#permalink]

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11 Sep 2017, 10:26
I found an alternative way to solve the problem and less intensive in calculations as you can see in the attached image:

Since the angle is 60º and the movement of the sections comes from the rotation of them, we will have 2 equilateral triangles formed with the vertex of initial and 60º position.

In the case that we wouldn't have any overlapping between the sections gap at 60º would be equal to the section length itself (green diagram), but since there is overlapping we have to subtract the overlapping length from the ideal gap/length of the section as seen in the blue diagram.

Thus, 28-2=6
Re: The figure represents the design of a drawbridge that spans a channel &nbs [#permalink] 11 Sep 2017, 10:26
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