Respuesta :

Answer:

[tex]PS=2\sqrt{6}[/tex]

Step-by-step explanation:

we are given triangle as

we know that

triangle PRS and triangle PQS are similar

so, the ratios of their sides must be equal

we get

[tex]\frac{RS}{PS}=\frac{PS}{QS}[/tex]

now, we are given

RS=4

QS=6

we can plug it

[tex]\frac{4}{PS}=\frac{PS}{6}[/tex]

[tex]PS^2=6\times 4[/tex]

[tex]PS^2=24[/tex]

now, we can solve for PS

[tex]PS=2\sqrt{6}[/tex]

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