Question

HELP PLEASE!!! I need help with this question!

Answer 1

Answer:

$\large\boxed{PS=10\sqrt5}$

Step-by-step explanation:

ΔPQS, ΔRQP and ΔRPS are similar (AA). Therefore the sides are in proportion:

$\dfrac{QR}{RP}=\dfrac{RP}{RS}$

We have:

$QR=5,\ RS=20$

Substitute:

$\dfrac{5}{RP}=\dfrc{RP}{20}$                cross multiply

$RP^2=(5)(20)\\\\RP^2=100\to RP=\sqrt{100}\\\\RP=10$

Use the Pythagorean theorem:

$PS^2=PR^2+RS^2$

Substitute:

$PS^2=10^2+20^2\\\\PS^2=100+400\\\\PS^2=500\to PS=\sqrt{500}\\\\PS=\sqrt{100\cdot5}\\\\PS=\sqrt{100}\cdot\sqrt5\\\\PS=10\sqrt5$