We have a triangle $\triangle ABC$ and a point $K$ on segment $\overline{BC}$ such that $AK$ is an altitude to $\triangle ABC$. If $AK = 6,$ $BK = 8$, and $CK = 6,$ then what is the perimeter of the triangle?
A
6
B 8 K 6 C
Since AK is an altitude....we can use the Pythagorean Theorem here
AB = √ [ BK^2 + AK^2 ] = √ [ 8^2 + 6^2] = √100 = 10
And AC = √ AK^2 + KC^2 ] = √ [ 6^2 + 6^2] = √ [ 2 * 6^2 ] = 6√2
So....the perimeter is
AB + BK + KC + AC =
10 + 8 + 6 + 6√2 =
24 + 6√2 units ≈ 32.49 units