Answer:
Therefore,
[tex]x=9\\\\y=7[/tex]
Step-by-step explanation:
Given:
D,E,F are the midpoints of side AB, BC,and AC such that
AB = 4x - 18
BC = 2x - 4
DF = x
FE = y
To Find:
x = ?
y = ?
Solution:
Midpoint Theorem:
The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.
E and F are Midpoint of Sides BC and AC, then
[tex]FE=\dfrac{1}{2}AB[/tex] ......By Midpoint Theorem
Substituting the values we get
[tex]x=\dfrac{1}{2}(4x-18)=2x-9\\\\2x-x=9\\\\x=9[/tex]
Similarly,
D and Fare Midpoint of Sides AB and AC, then
[tex]DF=\dfrac{1}{2}BC[/tex] ......By Midpoint Theorem
Substituting the values we get
[tex]y=\dfrac{1}{2}(2x-4)=x-2\\\\Substitute\ x=9\\\\y=9-2=7[/tex]
Therefore,
[tex]x=9\\\\y=7[/tex]
