The indicated measure, QR, is 1.3 unit.
triangles TRQ and TRS, both sharing a common side TR. Given that RS = 1.3 and TS = 4.7, and knowing that RS and RQ are similar sides (as they're corresponding sides in similar triangles), we can proceed to find QR.
Since TR is the common side shared by both triangles, and they're joined along this line, we can infer that TR divides the base of both triangles proportionally because they're similar triangles. This means we can set up a proportion to find QR.
Let
TS/ TR = RQ/ RS
because the triangles are similar by AA (angle-angle) similarity.
Plugging in the known values:
4.7 / TR= RQ/ 1.3
Given TR = RS + TS (since TR = RS + TS for triangles TRS and TRQ), and we know RS = 1.3 and TS = 4.7:
TR=1.3+4.7=6
To find RQ, rearrange the equation:
TR= QR- QT
6 = QR - 4.7
6- 4.7 = QR
QR= 1.3
Therefore, QR ≈ 1.3 units.