Question

question 6 of 10 given the median (overline{qr}) and trapezoid (mnop), what is the value of (x)? m (9x - 42) p q (x + 15) r n 30 o 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 $m=\frac{b_1 + b_2}{2}$, where $m$ is the median, $b_1$ and $b_2$ are the lengths of the bases. Here, the median $\overline{QR}=x + 15$, $b_1=9x-42$ and $b_2 = 30$.
So, $x + 15=\frac{(9x - 42)+30}{2}$.

Step2: Simplify the right - hand side

First, simplify the numerator of the right - hand side: $(9x - 42)+30=9x-12$. Then the equation becomes $x + 15=\frac{9x-12}{2}$.
Cross - multiply: $2(x + 15)=9x-12$.
Expand the left - hand side: $2x+30 = 9x-12$.

Step3: Solve for $x$

Subtract $2x$ from both sides: $30=9x-2x-12$.
Simplify: $30 = 7x-12$.
Add 12 to both sides: $30 + 12=7x$, so $42 = 7x$.
Divide both sides by 7: $x = 6$.

Answer:

A. 6