Question 529460
SPT is a right triangle with legs SP and PT of lengths 6 and 7 cm.
The length of hypotenuse ST is
{{{sqrt(6^2+7^2)=srt(85)}}}
Right triangle RVS (with 9 cm long hypotenuse SR) is similar, with angle RSV=RST congruent with angle PTS.
We are looking for the length of the short leg of that triangle, RV, opposite to angle RSV, corresponding to short leg SP in triangle SPT
{{{6/sqrt(85)=RV/9}}}
I get
{{{RV= 54sqrt(85)/85}}}
which sounds too complicated an answer for a classroom problem.