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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.
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.