Given:
The perpendicular bisector of the sides of triangle RST intersect at point P.
As RC is perpendicular bisector ST, it gives,
[tex]RS=RT\ldots.\ldots\text{.}\mathrm{}By\text{ pependicular bisector theorem}[/tex]
Consider the triangle RPT, PB is perpendicular bisector to RT.
Again by perpendicular bisector theorem,
[tex]\begin{gathered} RP=PT \\ 5x-12=3x+18 \\ 5x-3x=18+12 \\ 2x=30 \\ x=15 \end{gathered}[/tex]
It gives,
[tex]\begin{gathered} RP=5x-12=63 \\ PT=3x+18=63 \end{gathered}[/tex]
Using the same aurgument for triangle SPT,
[tex]\begin{gathered} SP=PT \\ SP=63 \end{gathered}[/tex]
Answer: SP = 63 inches
