Paula Whitmire

Assignment 6

Construct a triangle and its medians.

The triangle BCD below has centroid I and medians HC, BG, and DF.

A new triangle was contructed that has sides the same measure as the medians in the original triangle.

Length(Segment GE) = 2.18 inches
Length(Segment JK) = 2.18 inches
Length(Segment LK) = 1.75 inches
Length(Segment DF) = 1.75 inches
Length(Segment JL) = 2.17 inches
Length(Segment CH) = 2.17 inches

Area(Polygon JKL) = 1.74 square inches
Area(Polygon DBC) = 2.32 square inches
Perimeter(Polygon DBC) = 7.05 inches
Perimeter(Polygon JKL) = 6.10 inches

The ratio of the areas of the triangles is

1.74/2.32 = 0.75.

The ratio of the perimeters is 7.05/6.10 = 1.16

Now we will try some other triangles to see if this relationship with the areas remains .75 and the perimeters remains 1.16.

Length(Segment GE) = 1.08 inches
Length(Segment JK) = 1.08 inches
Length(Segment LK) = 3.02 inches
Length(Segment DF) = 3.02 inches
Length(Segment JL) = 3.37 inches
Length(Segment CH) = 3.37 inches
Area(Polygon JKL) = 1.62 square inches
Area(Polygon DBC) = 2.15 square inches
Perimeter(Polygon DBC) = 8.89 inches
Perimeter(Polygon JKL) = 7.47 inches

1.62/2.15 = 0.75
The ratio of the areas remains .75.

The ratio of the perimeters is 8.89/7.47 = 1.19. The ratio of the perimeters is very close but now exactly the same.

One more transformation shows that the ratios of perimeter and area appear the same.

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