Respuesta :
Answer:
Option B.
Step-by-step explanation:
It is given that ΔSRQ is a right angle triangle, ∠SRQ is right angle.
RT is altitude on side SQ, ST=9, TQ=16 and SR=x.
In ΔSRQ and ΔSTR,
[tex]m\angle S=m\angle S[/tex] (Reflexive property)
[tex]m\angle R=m\angle T[/tex] (Right angle)
By AA property of similarity,
[tex]\triangle SRQ\sim \triangle STR[/tex]
Corresponding parts of similar triangles are proportional.
[tex]\dfrac{SR}{SQ}=\dfrac{ST}{SR}[/tex]
Substitute the given values.
[tex]\dfrac{x}{9+16}=\dfrac{9}{x}[/tex]
[tex]\dfrac{x}{25}=\dfrac{9}{x}[/tex]
On cross multiplication we get
[tex]x^2=25\times 9[/tex]
[tex]x^2=225[/tex]
Taking square root on both sides.
[tex]x=\sqrt{225}[/tex]
[tex]x=15[/tex]
The value of x is 15. Therefore, the correct option is B.
