Question

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$\overline{uw}$ is a midsegment of $\triangle vxy$. if $xy = p - 4$ and $uw = p - 12$, what is the value of $p$?

Explanation:

Step1: Recall Midsegment Theorem

The midsegment of a triangle is parallel to the third side and half its length. So, \( UW=\frac{1}{2}XY \).

Step2: Substitute given expressions

Substitute \( XY = p - 4 \) and \( UW = p - 12 \) into the equation: \( p - 12=\frac{1}{2}(p - 4) \).

Step3: Solve for \( p \)

Multiply both sides by 2: \( 2(p - 12)=p - 4 \).
Expand left side: \( 2p - 24=p - 4 \).
Subtract \( p \) from both sides: \( p - 24=-4 \).
Add 24 to both sides: \( p = 20 \).

Answer:

\( p = 20 \)