Question

ux is the midsegment of the trapezoid stvw. if vw = 4z, ux = 6z + 2, and st = 7z + 5, what is the value of z?

Explanation:

Step1: Recall mid - segment formula

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

Step2: Substitute given expressions

Substitute $VW = 4z$, $UX=6z + 2$, and $ST = 7z + 5$ into the formula: $6z+2=\frac{4z+(7z + 5)}{2}$.

Step3: Multiply both sides by 2

$2(6z + 2)=4z+7z + 5$.
$12z+4=11z + 5$.

Step4: Solve for z

Subtract $11z$ from both sides: $12z-11z+4=11z-11z + 5$.
$z+4=5$.
Subtract 4 from both sides: $z=5 - 4$.

Answer:

$z = 1$