Question

given the median (overline{qr}) and trapezoid (mnop), what is the value of (x)? a. 6.5 b. 12.8 c. 8 d. 0 e. 2 f. cannot be determined

Explanation:

Step1: Recall trapezoid - median formula

The formula for the length of the median of a trapezoid is $\text{Median}=\frac{\text{Sum of bases}}{2}$. Here, the bases are $NO = 4x - 16$ and $MP=32$, and the median $QR=x + 16$. So, $x + 16=\frac{(4x - 16)+32}{2}$.

Step2: Simplify the right - hand side

First, simplify the numerator of the right - hand side: $(4x - 16)+32=4x+16$. Then the equation becomes $x + 16=\frac{4x + 16}{2}$. Since $\frac{4x + 16}{2}=2x + 8$, the equation is $x + 16=2x + 8$.

Step3: Solve for x

Subtract $x$ from both sides: $16=x + 8$. Then subtract 8 from both sides: $x=8$.

Answer:

C. 8