+1206 A right triangle has legs of length \(6\) and \(b\), and a hypotenuse of length \(c\). The perimeter of the triangle is \(18\). Compute \(c\).
+36916 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!
