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In triangle $ABC,$ $\angle B = 90^\circ.$  Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $AX = 15,$ and $BX = 15$.  What is $BC$?
 

 Dec 30, 2023
 #1
avatar+126665 
+1

A

     15

            X

      15

B                    C

 

AB =  sqrt (15^2 + 15^2)  = 15sqrt (2)

 

Triangles AXB and ABC  are similar

 

BX / AX =  BC / AB

 

15 / 15  = BC / 15sqrt (2)

 

1  = BC / 15sqrt (2)

 

15sqrt (2)  =  BC

 

cool cool cool

 Dec 30, 2023

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