Given that ps is a median of triangle pqr, find rq
a.6
b.12
c.19
d.38

The median triangle is a line segment that connects the vertex and the midpoint of the opposite side. Therefore, in the given, we can say that RS = QS

Equating RS and QS, we will find the value of X

RS = QS 
5x-11 = 2x+7
5x-2x = 7+11    ⇒ combine like terms
3x = 18             ⇒ divide both sides by 3 to get the x value 
x = 6

Find the value of RS and QS, in this, we will show that two are equal

5(6)-11 = 2(6)+7
19 = 19  ⇒ correct

Therefore RQ is the sum of RS and QS or simply twice the length of either segment

RQ = 19 x 2 = 19 + 19 = 38 (D)