XY = 17.
Because YW is a perpendicular bisector, we can say that TW and WZ are both equal to 3. It tells us that XZ is 12, so that means that XW must be 12+3 which equals 15.
It also tells us that YW is 8. So we can use the Pythagorean Theorem to find the hypotenuse of Triangle XWY. Thus, [tex] 15^{2} + 8^{2} = XY^{2} [/tex]
To solve this equation, square and add both of the terms on the right like this:
[tex]289 = XY^{2} [/tex]
And then take the square root of both sides. Your final answer should be:
XY = 17.
