Question

$\overline{sv}$ is the midsegment of the trapezoid $tuwx$. if $wx = -p + 40$, $sv = -p + 47$, and $tu = p + 6$, what is the value of $p$? $p = \square$

Explanation:

Step1: Recall the trapezoid midsegment theorem

The midsegment of a trapezoid is the average of the lengths of the two bases. So, \( SV=\frac{WX + TU}{2} \).

Step2: Substitute the given expressions

Substitute \( WX = -p + 40 \), \( SV = -p + 47 \), and \( TU = p + 6 \) into the formula:

$$ -p + 47=\frac{(-p + 40)+(p + 6)}{2} $$

Step3: Simplify the right - hand side

Simplify the numerator of the right - hand side: \( (-p + 40)+(p + 6)=-p + 40 + p+6 = 46 \). Then the equation becomes:

$$ -p + 47=\frac{46}{2} $$

$$ -p + 47 = 23 $$

Step4: Solve for p

Subtract 47 from both sides:

$$ -p=23 - 47 $$

$$ -p=-24 $$

Multiply both sides by - 1:

$$ p = 24 $$

Answer:

\( p = 24 \)