Question

1. points b, d, and f are mid - points 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 $EC = 32$ and $BF=2x - 10$, we substitute into the equation: $2x-10=\frac{1}{2}\times32$.

Step3: Simplify the right - hand side

$\frac{1}{2}\times32 = 16$, so the equation becomes $2x-10 = 16$.

Step4: Solve for $x$

Add 10 to both sides: $2x=16 + 10$, so $2x=26$. Then divide both sides by 2: $x = 13$.

Answer:

$x = 13$