Question

ux is the midsegment of the trapezoid vwyz. if yz = 11s, ux = s + 35, and vw = 15s + 22, what is the value of s? w x y z u v s =

Explanation:

Step1: Recall midsegment formula for trapezoid

The midsegment \( UX \) of a trapezoid \( VWYZ \) is equal to the average of the lengths of the two bases \( YZ \) and \( VW \). So the formula is \( UX=\frac{YZ + VW}{2} \).

Step2: Substitute the given expressions

Substitute \( YZ = 11s \), \( UX = s + 35 \), and \( VW = 15s + 22 \) into the formula:
\( s + 35=\frac{11s+(15s + 22)}{2} \)

Step3: Simplify the right - hand side

First, simplify the numerator of the right - hand side: \( 11s+15s + 22=26s + 22 \). Then the equation becomes \( s + 35=\frac{26s + 22}{2} \).
Divide \( 26s+22 \) by 2: \( \frac{26s+22}{2}=13s + 11 \). So the equation is \( s + 35=13s + 11 \).

Step4: Solve for s

Subtract \( s \) from both sides: \( 35=13s - s+11 \), which simplifies to \( 35 = 12s+11 \).
Subtract 11 from both sides: \( 35 - 11=12s \), so \( 24 = 12s \).
Divide both sides by 12: \( s=\frac{24}{12}=2 \).

Answer:

\( 2 \)