Answer: The required value of x is 22.
Step-by-step explanation: Given that B and F are the midpoints of the sides AC and AE of triangle ACE.
Also, BF = 2x and CE = 88.
We are to find the value of x.
Midpoint theorem : If a line segment joins the midpoints of any two sides of a triangle, then it is parallel to the third side and its length is equal to half of the length of the third side.
From triangle ACE, we have
B and F are the midpoints of the sides Ac and AE respectively, so BF will be parallel to CE and its length will ne half of the length of side CE.
Therefore,
[tex]BF=\dfrac{1}{2}\times CE\\\\\Rightarrow 2x=\dfrac{1}{2}\times88\\\\\Rightarrow 2x=44\\\\\Rightarrow x=\dfrac{44}{2}\\\\\Rightarrow x=22.[/tex]
Thus, the required value of x is 22.
