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A right triangle has legs of length \(6\) and \(b\), and a hypotenuse of length \(c\). The perimeter of the triangle is \(18\). Compute \(c\).

 Sep 23, 2018
 #1
avatar+16481 
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Pythag theorem

6^2 + b^2 = c^2

 

Given    6 + b + c = 18

      rearranged:  b=12-c      sub into pythag

 

6^2 + (12-c)^2 = c^2      expand

36 + 144 -24c + c^2 = c^2     simplify

180 =24c    solve

c = 7.5          then b = 18-7.5-6=4.5

 

Check   6^2 + 4.5^2 = 7.5^2  ??

              36 + 20.25 = 56.25           yes!

 Sep 24, 2018

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