Question

question 6 of 10 given the median (overline{qr}) and trapezoid (mnop), what

a. 6
b. 12
c. 8.5
d. 5
e. 7.5
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 $MP = 9x - 42$ and $NO=30$, and the median $QR=x + 15$. So, $x + 15=\frac{(9x - 42)+30}{2}$.

Step2: Cross - multiply

Multiply both sides of the equation by 2: $2(x + 15)=(9x - 42)+30$. Expand the left - hand side: $2x+30=9x - 42 + 30$.

Step3: Simplify the right - hand side

$2x+30=9x - 12$.

Step4: Move variables to one side

Subtract $2x$ from both sides: $30=9x-2x - 12$. So, $30 = 7x-12$.

Step5: Isolate the variable

Add 12 to both sides: $30 + 12=7x$, which gives $42 = 7x$.

Step6: Solve for x

Divide both sides by 7: $x=\frac{42}{7}=6$.

Answer:

A. 6