In the figure above, two security lights, L1 and L2 , are located 100

Question

https://gmatclub.com/forum/download/file.php?id=40047 In the figure above, two security lights, L1 and L2 , are located 100 feet apart. Each illuminates an area of radius 100 feet, and both are located 60 feet from a chain-link fence. What is the total length s of fence, in feet, illuminated by the two lights? (A) 260 (B) 240 (C) 220 (D) 200 (E) 180 2018-02-19_1000.png

pushpitkc · Accepted Answer

2018-02-19_1000.png The centers of both the circles are at a distance of 60 feet from the fence. Since the maximum distance that the light will travel is 100 feet, using the Pythagoras theorem the vertical distance can be calculated as \sqrt{100^2 - 60^2} = \sqrt{6400} = 80 But the small distance(marked in red) in the figure is not yet accounted for. The total length(s) of the fence which is illuminated by the lights is a little over 240. Therefore, Option A(260) is the only option available(> 240) and is our answer.

Hatakekakashi · Answer

100 . 80 . 60 triangle is formed wth the radius, fence and distance between fence n light source

three such triangles i.e length = 80+80+80 = 240

but some length isnt convered by three triangles thus >240

(a) imo

Kumayo · Answer

Answer: A (260).

The lights make a 90 degree angle with the fence and hence the vertical distance is 60 feet. The lights cover 100 feet of radius , which means the triangle made is a pythagorus one with 100, 60 and uknown variable (calculate it to get 80). Thus, the light L1 covers a distance of 2(80) on fence and the L2 covers a little more than 80, making a total of more than 240.

rahul0103 · Answer

The distance from L1 to L2 is 100. 
If we drop a perpendicular from L1 to the fence at P and from L2 to the fence at Q, then the distance between P & Q will be  100 . (L1 L2 Q P will be a rectangle)
100 .  80  . 60 triangle is formed with the radius, fence and distance between fence & light source. 
So total distance = 80+100+80 = 260

ScottTargetTestPrep · Answer

Solution: circles Overlapping1.png Let’s name the 4 intersection points of the fence with the circles as A, B, C, and D (see diagram above) and notice that we need to find the length of AD. Furthermore, let’s name one more point, E, where E is the midpoint of AC. We see that AEL1 is a right triangle; in fact it’s a 3-4-5 right triangle. Therefore, AE = 80 and AC = 2 x 80 = 160. Since BD = AC,then BD = 160 also. Notice that AD = AC + BD - BC, AD = 160 + 160 - BC = 320 - BC. If we can find the length of BC, we can determine the length of AD. However, we can see that BC has a length of less than 80 since it is less than EC, which has a length of exactly 80. Since BC < 80, therefore AD = 320 - BC will be greater than 240. Since the only answer choice that is greater than 240 is 260, choice A must be the correct answer. (Note: This means BC must be 60, but we will leave the readers to verify this on their own.) Alternate Solution: Circles Overlapping2.png Note that the distance S is equal to the distance from A to D. We can find the length of AB, the length of CD, and then the length of BC. First recognize triangle ABL1 as a 3-4-5 triangle, with lengths 60, 80, and 100. Thus, the length AB = 80. This is the same as the length CD because triangle DCL2 is also a 3-4-5 triangle, so CD = 80. Note that the distance from B to C is equal to the distance from L1 to L2, and this is given as 100. Thus, the total distance is 80 + 100 + 80 = 260. Answer: A

Fdambro294 · Answer

It's easier if you 1st take the 2 Triangles out of the Circle and Flip them over so they are easy to look at it.

Rule - Since the 2 Triangles are Isosceles Triangles with Sides = Radius = 100, the Median from the Apex Vertex to the Non-Equal Side will Bisect that Opposite Non-Equal Side.

L1 and L2 being 60 feet away from the Fence = the Straight Line Distance dropped from the Apex Vertices (L1 and L2) and drawn Perpendicular to the Opposite NON-Equal Side = the Median that Bisects the Opp. Side in HALF = which is equal to the Height of 60

Now 2 Right Triangles are created in each of the Triangles.

1 Leg = 60 and Hypotenuse = 100

all 4 Sub Triangles are 3-4-5 Common Right Triangle. Thus, for each of the 4 Sub Triangles, the Distance Length from the Edge of the Triangle to the Median Point on the Bisected Side is = 80.

The Distance from the Median Point to the other Median Point between the 2 Triangles = Distance from the L1 Vertex to the L2 Vertex = Given as 100

80 + 80 + 100 = 260

Answer A

EDIT: the 2nd Picture above in Scott's Post. (didn't see it at first lol)

bumpbot · Answer

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In the figure above, two security lights, L1 and L2 , are located 100

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