Question

ux is the midsegment of the trapezoid stvw. if st = y, ux = -y + 100, and vw = 3y - 40, what is the value of y?

Explanation:

Step1: Recall mid - segment formula

The formula for the length of the mid - segment of a trapezoid is $UX=\frac{ST + VW}{2}$.

Step2: Substitute given values

Substitute $ST = y$, $UX=-y + 100$, and $VW = 3y-40$ into the formula: $-y + 100=\frac{y+(3y - 40)}{2}$.

Step3: Simplify the right - hand side

First, simplify the numerator of the right - hand side: $y+(3y - 40)=4y-40$. So the equation becomes $-y + 100=\frac{4y-40}{2}$. And $\frac{4y-40}{2}=2y-20$. So we have $-y + 100=2y-20$.

Step4: Solve for y

Add y to both sides: $100=2y-20 + y$, which simplifies to $100=3y-20$. Then add 20 to both sides: $100 + 20=3y$, so $120 = 3y$. Divide both sides by 3: $y = 40$.

Answer:

$40$