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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.

(2 points)

1 answer

To find the distance between campsites F and G, we can use proportionality of the triangles formed by the intersecting segments.

Let's set up the proportion using the measurements given in the diagram:
(60 + 30) / 60 = x / 90

Simplify the proportion:
90 / 60 = x / 90
3/2 = x / 90

Cross multiply to solve for x:
2x = 3 * 90
2x = 270
x = 270 / 2
x = 135

Therefore, the distance between campsites F and G is 135 units.