A right triangle has legs of length 6 and b, and a hypotenuse of length c. The perimeter of the triangle is 15. Compute c.
+9519 By Pythagorean theorem, \(6^2 + b^2 = c^2\).
Perimeter is 15 means \(6 + b + c = 15\).
Then \(\begin{cases}c^2 - b^2 = 36\\b + c = 9\end{cases}\). Note that c^2 - b^2 = (c - b)(b + c) = 9(c - b). Therefore:
\(9(c - b) = 36\\ c - b = 4\)
Consider \(2c = (b + c) + (c - b)\).
\(2c = 9 + 4\\ c = \dfrac{13}2\)
