Geometry

The braces are the hypotenuse of a right triangle with legs of 40 and 55 in

brace² = 40²  + 55²

brace =~~ 68 in

 

A carpenter builds a rectangular bookcase that is 40 inches long and 55 inches tall. The carpenter uses two braces along the diagonals to support the bookcase.      

 

If you draw this, or just picture it in your mind, you recognize that the diagonal brace forms the hypotenuse of a right triangle whose legs are 40 inches and 55 inches.  So, it's possible just to use Pythagoras' Theorem.  

 

Call the 40 inch side as "a"     Call the 55 inch side as "b"     Call the brace (hypotenuse) as "c"   

 

By the theorem, a² + b²  =  c²   

 

So                      c²  =  40² + 55² 

 

                          c²  =  1600 + 3025  =  4625   

 

                          c   =  sqrt(4625)   

 

                          c   =  +68.007   

 

Thus, the length of each brace is 68 inches   

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