Question

1. points b, d, and f are midpoints of the sides of △ace. ec = 32 and bf = 2x - 10. find the value of x. 16 21 13 42

Explanation:

Step1: Apply mid - segment theorem

In $\triangle ACE$, since $B$ and $F$ are mid - points of two sides, by the mid - segment theorem, $BF=\frac{1}{2}EC$.

Step2: Substitute given values

Given $EC = 32$, then $BF=\frac{1}{2}\times32 = 16$.

Step3: Solve for x

Since $BF = 2x-10$ and $BF = 16$, we set up the equation $2x-10=16$.
Add 10 to both sides: $2x=16 + 10=26$.
Divide both sides by 2: $x = 13$.

Answer:

13