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In the diagram, angles PQR and PST are right angles. If PR = 35, PT = 11, and QT = 10, then what is PS?

https://latex.artofproblemsolving.com/9/8/a/98a4a34141ce8e1a7a9489d6cc79ee967fd8c6d6.png

 Dec 16, 2019
 #1
avatar+23809 
+2

In the diagram, angles PQR and PST are right angles. If PR = 35, PT = 11, and QT = 10, then what is PS?

 

Let PS = x

 

\(\begin{array}{|rcll|} \hline \dfrac{x}{11} &=& \dfrac{21}{35} \\\\ x &=& \dfrac{11*21}{35} \\\\ \mathbf{x} &=& \mathbf{6.6} \\ \hline \end{array}\)

 

PS is 6.6

 

laugh

 Dec 16, 2019
 #2
avatar+106519 
+1

Note that triangle  RQP   is similar to triangle  TSP

 

Therefore

 

 QP / RP  = SP / TP

 

{PT +QT ]  / QP  = PS/ TP

 

[11 + 10] / 35  =  PS /  11

 

21 / 35 =  PS / 11

 

21 * 11/ 35  = PS

 

(21/35)* 11   =PS

 

(3/5) * 11  = PS

 

33/5  =  PS  =  6.6

 

 

cool cool cool

 Dec 17, 2019

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