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:

`(SR)/(PO)=(1)/(2)\rightarrow(5x-38)/(7a-49)=(1)/(2)\rightarrow5x-38=(7a-49)/(2)\rightarrow5x=(7a-49)/(2)+38\rightarrow5x=(7a+27)/(2)\rightarrow x=(7a+27)/(10)`

So, RS is:

`RS=5x-38\rightarrow RS=(7a+27)/(2)-38\rightarrow RS=(7a+27-76)/(2)\rightarrow RS=(7a-49)/(2)`