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.
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.
\(6^2 + (12-c)^2 = c^2\)
\(36 + 144-24c + c^2 = c^2\)
\(180 -24c = 0\)
\(24c = 180\)
\(c = 180/24 = 30/4 = 15/2\)