Question

ux is the midsegment of the trapezoid vwyz. if vw = 45 and ux = 58, what is yz?

Explanation:

Step1: Recall mid - segment formula

The formula for the length of the mid - segment of a trapezoid is $UX=\frac{VW + YZ}{2}$, where $UX$ is the mid - segment, $VW$ is one base, and $YZ$ is the other base.

Step2: Rearrange the formula to solve for $YZ$

Multiply both sides of the equation $UX=\frac{VW + YZ}{2}$ by 2 to get $2UX=VW + YZ$. Then subtract $VW$ from both sides: $YZ = 2UX-VW$.

Step3: Substitute given values

We know that $VW = 45$ and $UX = 58$. Substitute these values into the formula $YZ = 2UX-VW$. So $YZ=2\times58 - 45$.
$YZ = 116-45$.
$YZ = 71$.

Answer:

$71$