Answer:
x=50
Step-by-step explanation:
The picture of the question in the attached figure
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional
In this problem
Triangle RQS and Triangle RPT are similar by AA Similarity Theorem
so
[tex]\frac{RP}{RQ}=\frac{RT}{RS}[/tex]
we have
[tex]RP=PQ+QR=9+3=12\ units\\RQ=QR=3\ units\\RS=17\ units[/tex]
substitute the given values
[tex]\frac{12}{3}=\frac{RT}{17}[/tex]
solve for RT
[tex]RT=17(4)=68\ units[/tex]
Remember that
[tex]RT=RS+ST[/tex]
we have
[tex]RT=68\ units\\RS=17\ units\\ST=x+1[/tex]
substitute
[tex]68=17+x+1[/tex]
solve for x
[tex]x=68-18\\x=50[/tex]
