## Elementary Geometry for College Students (7th Edition)

$MR = 125$ $RP = 125$ $MP = 250$
The diagonals of a parallelogram bisect each other. Therefore the point R is the midpoint of $\overline{MP}$ We can find the value of $a$: $MP = 2\times MR$ $12a+34 = 2\times 5(a+7)$ $12a+34 = 10a+70$ $2a = 36$ $a = 18$ We can find $MR$: $MR = 5(a+7) = 5(18+7) = 125$ We can find $RP$: $RP = MR = 125$ We can find $MP$: $MP = MR + RP = 125 + 125 = 250$