Question

ux is the midsegment of the trapezoid tvwy. if ty = 19 and ux = 31, what is vw? vw =

Explanation:

Step1: Recall mid - segment formula

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

Step2: Rearrange the formula to solve for $VW$

Starting from $UX=\frac{TY + VW}{2}$, we multiply both sides by 2: $2UX=TY + VW$. Then we subtract $TY$ from both sides: $VW = 2UX−TY$.

Step3: Substitute the given values

We know that $TY = 19$ and $UX = 31$. Substituting these values into the formula $VW = 2UX−TY$, we get $VW=2\times31−19$.

Step4: Calculate the value of $VW$

First, calculate $2\times31 = 62$. Then, $62−19=43$.

Answer:

$43$