According the triangle midsegment theorem, the length of AC in the given triangle is 40 units.
What is the Midsegment of a Triangle?
The midsegment of a triangle is defined as the line segment that intersects two sides of a triangle at their midpoints. This means that, the sides they intersect is bisected forming two equal halves.
In a triangle, there are three midsegments in the triangle.
The image given in the attachment below, the midsegments of the triangle are: DF, FB, and BD.
All midsegments are parallel to the third sides of a triangle.
Using the triangle midsegment theorem, the length of the midsegment (i,e. DF) is parallel to the third side (i.e. AC) and also half the length of the third side (AC).
We are given the following:
EC = 30
DF = 20
Applying the triangle midsegment theorem, we have,
DF = 1/2(AC)
Substitute;
20 = 1/2(AC)
2(20) = AC
40 = AC
AC = 40 units.
According the triangle midsegment theorem, the length of AC in the given triangle is 40 units.
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