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:

Set up the trapezoid midsegment equation

$$ QR = \frac{NO + MP}{2} $$

$$ x + 16 = \frac{(4x - 16) + 32}{2} $$

Simplify and solve for x

$$ x + 16 = \frac{4x + 16}{2} $$

$$ x + 16 = 2x + 8 $$

$$ 16 - 8 = 2x - x $$

$$ x = 8 $$

Answer:

• A. 6.5
• B. 12.8
• C. 8 (Correct answer)
• D. 0
• E. 2
• F. Cannot be determined