1 Answer

Toyota Supra · Answer 1 · 2020-05-02T13:16:28+0000

Answer:

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

Explanation:

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

(QR)/(RP)=(RP)/(RS)

We have:

$QR=5,\ RS=20$

Substitute:

$(5)/(RP)=\dfrc{RP}{20}$ cross multiply

$RP^2=(5)(20)\\\\RP^2=100\to RP=√(100)\\\\RP=10$

Use the Pythagorean theorem:

PS^2=PR^2+RS^2

Substitute:

$PS^2=10^2+20^2\\\\PS^2=100+400\\\\PS^2=500\to PS=√(500)\\\\PS=√(100\cdot5)\\\\PS=√(100)\cdot\sqrt5\\\\PS=10\sqrt5$

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