Let's begin with recalling the Triangle Angle Bisector Theorem.
An angle bisector in a triangle separates the opposite side into two segments that are proportional to the lengths of the other two sides.
Now let's look at the given picture. Let x be the length of PS and y be the length of SR.
Since QS is an angle bisector of ∠Q, we can write a proportion.
x/y=22.4/29.2
We also know that the perimeter of this triangle is 94 units. Let's use this information to write a second equation. Recall that a perimeter is a sum of all side lengths.
22.4+29.2+( x+ y)= 94
Let's create a system of equations using the two equations we found above.
xy= 22.429.2 & (I) 22.4+29.2+(x+y)=94 & (II)
First, we can simplify them a little bit before using the Substitution Method.
Since we isolated x in the second equation, we can solve this system using the Substitution Method. To do this, let's substitute 42.4-y for x in the first equation.
