Question

In the diagram below of triangle OPQ, R is the midpoint of OQ and S is themidpoint of PQ .If RS = 5x – 38, and OP=7a – 49, what is the measure ofRS?

Answer 1

First, lets draw our triangle:

-By the relation side-angle-side we can see that the triangle QSR and QPO are similar, since QS/QP=1/2 and QR/QO=1/2, so we have that:

$\frac{SR}{PO}=\frac{1}{2}\rightarrow\frac{5x-38}{7a-49}=\frac{1}{2}\rightarrow5x-38=\frac{7a-49}{2}\rightarrow5x=\frac{7a-49}{2}+38\rightarrow5x=\frac{7a+27}{2}\rightarrow x=\frac{7a+27}{10}$

So, RS is:

$RS=5x-38\rightarrow RS=\frac{7a+27}{2}-38\rightarrow RS=\frac{7a+27-76}{2}\rightarrow RS=\frac{7a-49}{2}$