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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