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

Question

https://gmatclub.com/forum/download/file.php?id=25329 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 1.png Kudos for a correct solution .

PareshGmat · Accepted Answer

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 [ 10.52 KiB | Viewed 8244 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

BrentGMATPrepNow · Answer

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:
 https://i.imgur.com/ICgsiTI.png

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 .
 https://i.imgur.com/zbket8u.png

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

WoundedTiger · Answer

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 8110 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

GMATinsight · Answer

Answer: Option B

Check solution

sahilvijay · Answer

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

)

Bunuel · Answer

This works for 1 week till the OA is revealed.

sahilvijay · Answer

Okay i was not knowing this.

EddyEd · Answer

I found an alternative way to solve the problem and less intensive in calculations as you can see in the attached image:

https://i.imgur.com/S7DPWxv.png

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

bumpbot · Answer

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

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

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