Question

u and x are the midpoints of the legs, \\(\overline{tv}\\) and \\(\overline{sw}\\), of trapezoid stvw. if \\(ux = 70\\) and \\(vw = 86\\), what is \\(st\\)? \\(st = \square\\)

Explanation:

Step1: Recall the midsegment theorem for trapezoids

The midsegment (or median) of a trapezoid is the segment that connects the midpoints of the legs, and its length is the average of the lengths of the two bases. The formula is \( UX=\frac{ST + VW}{2} \), where \( UX \) is the midsegment, \( ST \) and \( VW \) are the two bases of the trapezoid.

Step2: Substitute the known values into the formula

We know that \( UX = 70 \) and \( VW=86 \). Substituting these values into the formula \( 70=\frac{ST + 86}{2} \).

Step3: Solve for \( ST \)

First, multiply both sides of the equation by 2: \( 70\times2=ST + 86 \), which simplifies to \( 140=ST + 86 \). Then, subtract 86 from both sides: \( ST=140 - 86 \).

Step4: Calculate the result

\( 140-86 = 54 \).

Answer:

\( 54 \)