ABED is a square with sides of length 6. If point C is the midpoint of ED, what is the perimeter of ABCD?

Answer 1

We know that the length of AB is 6, the length of CD is 3 (Since C is the midpoint of ED), and the length of BD is 6. AC is the hypotenuse of the right triangle AEC, which has legs of length 6 and 3. Therefore, the length of AC is:

sqrt(6² + 3²) = 3 * sqrt(5)

Therefore, the perimeter is 6 + 6 + 3 + 3sqrt(5) = 15 + 3sqrt(5)