Answer:
[tex]\large\boxed{PS=10\sqrt5}[/tex]
Step-by-step explanation:
ΔPQS, ΔRQP and ΔRPS are similar (AA). Therefore the sides are in proportion:
[tex]\dfrac{QR}{RP}=\dfrac{RP}{RS}[/tex]
We have:
[tex]QR=5,\ RS=20[/tex]
Substitute:
[tex]\dfrac{5}{RP}=\dfrc{RP}{20}[/tex] cross multiply
[tex]RP^2=(5)(20)\\\\RP^2=100\to RP=\sqrt{100}\\\\RP=10[/tex]
Use the Pythagorean theorem:
[tex]PS^2=PR^2+RS^2[/tex]
Substitute:
[tex]PS^2=10^2+20^2\\\\PS^2=100+400\\\\PS^2=500\to PS=\sqrt{500}\\\\PS=\sqrt{100\cdot5}\\\\PS=\sqrt{100}\cdot\sqrt5\\\\PS=10\sqrt5[/tex]
