Question

question 24 of 27
mnop is a trapezoid with median (overline{qr}). find (x).

a. (x = 7)
b. (x = 5)
c. (x = 3)
d. (x = 6)

Explanation:

Step1: Recall the trapezoid median formula

The median of a trapezoid is the average of the lengths of the two bases. So, if \( QR \) is the median, \( NO \) and \( MP \) are the bases, then \( QR=\frac{NO + MP}{2} \).
Given \( NO = 8 \), \( QR = 12 \), and \( MP=2x + 6 \), we substitute into the formula: \( 12=\frac{8+(2x + 6)}{2} \).

Step2: Solve the equation for \( x \)

First, multiply both sides of the equation by 2 to eliminate the denominator: \( 12\times2=8 + 2x+6 \).
Simplify the left - hand side and the right - hand side: \( 24=2x + 14 \).
Then, subtract 14 from both sides: \( 24-14 = 2x \), which gives \( 10 = 2x \).
Finally, divide both sides by 2: \( x=\frac{10}{2}=5 \).

Answer:

B. \( x = 5 \)