In the diagram below, we have line QR parallel to line ST, PQ = 8, QS = 6, and PT = 12. Find PR
+129840 We are using the fact that the line segment QR drawn parallel to ST divides the other sides of the triangle into similar ratios....that is
PQ / QS = PR / RT .....and.....
PQ/ [ PQ + QS] = PR/ [ PR + RT]
8 / [ 14] = PR / [ 12 ] multiply both sides by 12
96 / 14 = PR = 48 / 7
Check :
PT - PR = 12 - 48/7 = [84 - 48] / 7 = 36/7 = RT
And
PQ / QS = PR /RT
8 / 6 = [48 / 7] / [ 36 / 7]
8 / 6 = 48 / 36
8 / 6 = 8 / 6
