## Elementary Geometry for College Students (6th Edition)

$OP=7$, $MN=23$
Theorem 4.4.3: The length of the median of a trapezoid equals one-half the sum of the lengths of the two bases. $\frac{base+base}{2}=median$ $\frac{(3x+2)+(2x-7)}{2}=15$ Combine like terms in the numerator... $\frac{5x-5}{2}=15$ Multiply both sides by 2... $5x-5=30$ Add 5 to both sides... $5x=35$ Divide both sides by 5... $x=7$ $MN=3x+2=3(7)+2=23$ $OP=2x-7=2(7)-7=7$