+0

-1
132
3
+128

In the diagram below we have QR is parallel to ST, PQ=8, QS=6, and PT=10.5

Find PR

https://latex.artofproblemsolving.com/7/0/2/70221f74557d9f47f65c187cf798e80474ed0974.png

Oct 8, 2019

#1
+999
0

Please don't post AoPS questions (or at least spam them).

Use the Message Board, or ask a friend! Only if you really need the answer, ask for hints.

PQR and PST are similar. PQ + QS = 14, and PQ = 8, so PQ is 8/14, or 4/7, the length of PS.

Same proportion for PT. PT is 10.5, and PR is 4/7 of that length. Can you find out from here?

Oct 8, 2019
#3
+2547
0

Yes you must be taking an AoPS class! How lucky of you Saketh :D

Just try the problems they give you first, and try your best. And maybe post your attempted solution with the question.

*You will get smarter (trust me)*

CalculatorUser  Oct 9, 2019
#2
+106539
+2

QR  splits the sides PS and PT proportionally.....

So

PQ / PR  =  PS / PT

PQ / PR  = [ PQ + QS] / PT

8/ PR  =  [ 8+ 6 ]  / 10.5

8 /PR  = 14/10.5

PR / 8  =  10.5 / 14

PR  =  8 (10.5) /14  =  6

Oct 9, 2019