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

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Bunuel
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The figure represents the design of a drawbridge that spans a channel [#permalink] New post   20 Jan 2015, 07:00
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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

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PareshGmat
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Re: The figure represents the design of a drawbridge that spans a channel [#permalink] New post   22 Jan 2015, 19:09
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Answer = B = 26

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
1.png [ 10.52 KiB | Viewed 7389 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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Re: The figure represents the design of a drawbridge that spans a channel [#permalink] New post   19 Aug 2020, 07:11
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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

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1.png


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The two raisable sections are equal in length and overlap each other by a measure of 2 meters
The bridge spans a distance of 54 meters.
So, if both sections were 27 meters long, there would be no overlap.
Since the sections overlap by 2 meters, we know that each section is 28 meters long.
So, our diagram looks like this:



If we draw vertical lines from the tips of each section, you see that we have special 30-60-90 triangles hiding in our diagram.
In the each of the right triangles, the hypotenuse has length 28
So, the lengths of the sides opposite the 30 degree angles must be 14.



To find the value of x, we can write the following equation: 14 + x + 14 = 54
Simplify: x + 28 = 54
Subtract 28 from both sides of the equation to get: x = 26

Answer: B

Cheers,
Brent
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Re: The figure represents the design of a drawbridge that spans a channel [#permalink] New post   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
1.png [ 12.08 KiB | Viewed 7287 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] New post   11 Sep 2017, 03:40
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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

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The attachment 1.png is no longer available


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Bunuel => awaiting kudos for correct solution.(mentioning first time though 8-) )
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The figure represents the design of a drawbridge that spans a channel [#permalink] New post   12 Nov 2016, 00:58
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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

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Answer: Option B

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Re: The figure represents the design of a drawbridge that spans a channel [#permalink] New post   11 Sep 2017, 03:44
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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

Show Spoiler
Attachment:
1.png


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Bunuel => awaiting kudos for correct solution.(mentioning first time though 8-) )


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

Show Spoiler
Attachment:
1.png


Kudos for a correct solution.



Bunuel => awaiting kudos for correct solution.(mentioning first time though 8-) )


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] New post   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
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Re: The figure represents the design of a drawbridge that spans a channel [#permalink] New post   01 Dec 2022, 06:32
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Re: The figure represents the design of a drawbridge that spans a channel [#permalink]
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