+84 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.
thanks :D
+499 Algebra will be our friend in this problem. We already have our variables to work with, so let's set up some equations:
\(6^2 + b^2 = c^2\) by Pythagorean theorem
We also have that the perimeter is 18, meaning:
\(6+b+c = 18\)
\(b+c = 12\)
\(b = 12-c\)
Substitute back into our equation from the Pythagorean theorem, and we can solve for the value of c.
\(6^2 + (12-c)^2 = c^2\)
\(36 + 144-24c + c^2 = c^2\)
\(180 -24c = 0\)
\(24c = 180\)
\(c = 180/24 = 30/4 = 15/2\)
