Question

Triangle Proportionality and Angle Bisector TheoremsNeed answers and help please

Answer 1

Step 1:

Triangle PRS is similar QRS.

PR is similar to RQ

PS is similar to QS

Step 2:

PR = 14 - x

RQ = x

PS = 6

QS = 4

Step 3:

`\begin{gathered} (PR)/(QR)\text{ = }(PS)/(QS) \\ \frac{14\text{ - x}}{x}\text{ = }(6)/(4) \\ \frac{14\text{ - x}}{x}\text{ = }(3)/(2) \\ 2(14\text{ - x) = 3x} \\ 28\text{ - 2x = 3x} \\ 28\text{ = 3x + 2x} \\ 28\text{ = 5x} \\ x\text{ = }(28)/(5) \\ x\text{ = 5.6} \end{gathered}`