User:Pepper2831
Solution 3 (Pythagorean Theorem) Assign ZA as , then AY as . Assign XM as and MY as . Since triangles WXM and WZA are together, we can say , so . Then therefore, XM is and MY has length . We can use the Pythagorean theorem to find WM, which is actually . We don't factor it yet - we are going to find again using the Pythagorean Theorem. Similarly, finding MA is just the square root of the squares of AY and MY individually, or . Then simply, WA is really .
Now we have the three sides of the right triangle: , , and . Per the Pythagorean theorem again, we can see . Combining like terms gives us , then dividing by 8 gives . As this elementary and well-known quadratic gives us the roots of and , we can see it is a bit weird to have , as then point Z is point A. So we'll assume . We have two legs of the triangle by plugging in the sides with x in them, given that : and . We should know that , and Dividing by 2 reveals us our answer:
~pepper2831