Step 1
In the right triangle RTQ
Find the value of [tex]RQ^{2}[/tex]
Applying the Pythagorean Theorem
[tex]RQ^{2} =RT^{2}+TQ^{2}[/tex]
we have
[tex]RT=x\ units \\TQ=16\ units[/tex]
substitute the values
[tex]RQ^{2} =x^{2}+16^{2}[/tex]
[tex]RQ^{2} =x^{2}+256[/tex]
Step 2
In the right triangle RST
Find the value of [tex]RS^{2}[/tex]
Applying the Pythagorean Theorem
[tex]RS^{2} =RT^{2}+ST^{2}[/tex]
we have
[tex]RT=x\ units \\ST=9\ units[/tex]
substitute the values
[tex]RS^{2} =x^{2}+9^{2}[/tex]
[tex]RS^{2}=x^{2}+81[/tex]
Step 3
In the right triangle RSQ
Find the value of x
Applying the Pythagorean Theorem
[tex]SQ^{2} =RS^{2}+RQ^{2}[/tex]
we have
[tex]RS^{2}=(x^{2}+81)\ units^2\\RQ^{2}=(x^{2}+256)\ units^2[/tex]
[tex]SQ^{2}=(16+9)^2=625\ units^2[/tex]
substitute the values
[tex]625=(x^{2}+81)+(x^{2}+256)[/tex]
[tex]625=(2x^{2}+337)[/tex]
[tex]2x^{2}=625-337[/tex]
[tex]2x^{2}=288[/tex]
[tex]x^{2}=144[/tex]
[tex]x=12\ units[/tex]
therefore
the answer is
[tex]x=12\ units[/tex]
