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.

1 answer

To find the distance between campsites F and G, we need to use a proportional relationship between the two triangles.

Let's call the distance between campsite F and the point where the segments intersect X, and the distance between campsite G and the point where the segments intersect Y.

In triangle FDE, we have the proportions:
EF/DE = X/50

In triangle GDF, we have the proportions:
DG/DF = Y/30

From the given measurements in the diagram, we have:
EF = 70, DE = 50, DG = 90, DF = 30

Using these proportions, we can solve for X and Y:

EF/DE = X/50
70/50 = X/50
X = 70

DG/DF = Y/30
90/30 = Y/30
Y = 90

Therefore, the distance between campsites F and G is X + Y which is:
70 + 90 = 160

So, the distance between the two campsites is 160 units.