A right triangle has legs of length 6 and b and a hypotenuse of length c. The perimeter of the triangle is 24. Compute c.
+118 Firstly, we write \(b^2+36=c^2\). Then, we write \(b+c=18\). These are from the two given conditions. We manipulate the first equation to \((b+c)(b-c)=-36\). Plugging in our value, we find that \(b-c=-2\). Therefore, \(b=8, c=\boxed{10}\).
+118 Firstly, we write \(b^2+36=c^2\). Then, we write \(b+c=18\). These are from the two given conditions. We manipulate the first equation to \((b+c)(b-c)=-36\). Plugging in our value, we find that \(b-c=-2\). Therefore, \(b=8, c=\boxed{10}\).
