I think the only condition where AC and BD are perpendicular is: when the quadrilateral is a square. One need to draw the shape of the quadrilateral with having the left bottom corner of it at the origin of X and Y coordinate system.
After you draw the shape with (AB=15 unites), you will figure out that the other 3 sides are also 15 units because it’s a square. From the figure you can easily say that the coordinates for T is (7.5, 7.5) , but since the question asked you to calculate, then use the midpoint equation for the line BDT to calculate the coordinate of point T as: X = (X1+X2)/2 and Y = (Y1+Y2)/2
You can get the X1, Y1, X2, and Y2 from the two corners of equilateral.
I guess this will be the answer.