Pythagoras

 

What is the measure of x?     

 

I'm saying that the triangles are similar, so     

 

3 : z  =  z : 30      i.e., ratio of short side to hypotenuse of small triangle     

                           equals ratio of short side to hypotenuse of large triangle.     

                           If they are not similar, don't bother reading any further.    

 

                                    3 / z  =  z / 30     

 

crossmultiply to get      z² =  90     

 

by Pythagoras              x²  =  30² – z²     

                                     x²  =  900 – 90     

                                     x   =  sqrt(810)     

 

This answer looks counterintuitive because the figure is not drawn to scale.     

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