To find the distance between the two campsites, we can use the concept of similar triangles.
Let's denote the distance between Campsite F and the intersecting point as x.
Using the concept of similar triangles, we can set up the following proportion:
(Length of DF) / (Length of AC) = (Length of GF) / (Length of BC)
Plugging in the given measurements, we have:
(4 + x) / 25 = (8 + 2x) / 40
Cross multiplying, we have:
(4 + x) * 40 = (8 + 2x) * 25
Expanding both sides, we have:
160 + 40x = 200 + 50x
Rearranging the equation, we have:
10x = 40
Dividing both sides by 10, we get:
x = 4
Therefore, the distance between the two campsites (FG) is 4 + 8 + 2(4) = 4 + 8 + 8 = 20 units.
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The diagram shows two campsites on opposite ends of a lake and two triangles formed by intersecting segments from the campsites.
Campsites F and G are on opposite sides of a lake. A survey crew made the measurements shown on the diagram. What is the distance between the two campsites? The diagram is not drawn to scale. The triangles are proportional.
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