Answer:
x = 15
Step-by-step explanation:
ΔRTS and ΔQRS are similar. Therefore the sides are in proportion:
[tex]\dfrac{RS}{SQ}=\dfrac{ST}{RS}[/tex]
We have:
[tex]RS=x\\SQ=9+16=25\\ST=9\\RS=x[/tex]
Substitute:
[tex]\dfrac{x}{25}=\dfrac{9}{x}[/tex] cross multiply
[tex]x^2=(25)(9)\\\\x^2=225\to x=\sqrt{225}\\\\x=15[/tex]
