Answer:
Option D is correct.
FE = 13 units
Step-by-step explanation:
As per the statement: F is the midpoint of AB and E is the midpoint of AC.
If [tex]FE = x+5 units[/tex] and
By midpoint theorem of line states that the points on a line segment equally distant from the two endpoints.
Then, by midpoint theorem of line we have;
[tex]FE =\frac{1}{2}BC[/tex]
Substitute the given values we have;
[tex]x+5 = \frac{1}{2}(3x+2)[/tex]
Multiply both sides by 2 we getl;
[tex]2(x+5) = 3x+2[/tex]
Using distributive property:
[tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]
2x + 10 = 3x+ 2
Subtract 2 from both sides we get;
2x + 8 = 3x
Subtract 2x from both sides we have;
8 = x
or
x =8 units.
We have to find the value of FE.
FE = x +5 = 8+5 =13 units
Therefore, the value of FE is, 13
