Question

Question 20 - 5 PointsJon 14, 10:17:14 PM?In APRQ shown below, point S is on QR, and point T is on PR so thatZPQR = ZSTR. If PQ = 104, ST = 40, and RP = 130, find the length ofRS. Figures are not necessarily drawn to scale.TQSRoo

Answer 1

Since we are told that angles PQR and STR are congruent, we can draw each triangle apart from each other, as follows

Since they have one congruent angle, we can see that one triangle is a drawn as scale from the other. Having the congruent angle in the same position (left most corner of each triangle) allows us to relate the sides of each triangle regarding their positions with respect to the congruent angle. In the picture we have draw colored lines for each pair of related sides. Since they are similar triangles, we can establish the following equation

`(ST)/(PQ)=(SR)/(PR)`

We have PQ=104, ST =40 and PR = 130. Thus

`(SR)/(130)=(40)/(104)`

So, by multiplying both sides by 130 we get

`SR=(130\cdot40)/(104)=(5200)/(104)=50`