In the given diagram, we see that quadrilateral QRST is a kite. This means that it has two pairs of congruent adjacent sides, and the diagonals intersect at a right angle.
To find SU, we need to first identify which line segment is SU. Looking at the diagram, we see that SU is the diagonal that is perpendicular to RT and passes through the intersection point of the diagonals. Let's call this intersection point X.
Since QRST is a kite, we know that the diagonals QS and RT are perpendicular and bisect each other. This means that they divide the kite into four congruent triangles.
Therefore, we can find the length of SX by using the Pythagorean theorem in one of these triangles. Let's use triangle QXS:
QS = QR = 12 (since opposite sides of a kite are congruent)
QS/2 = 6 (since the diagonals bisect each other)
QX = QT - TX = 16 - 7 = 9
QX^2 + SX^2 = QS^2/4
9^2 + SX^2 = 12^2/4
81 + SX^2 = 36
SX^2 = 36 - 81
SX^2 = -45
We cannot take the square root of a negative number, so this means there is no real solution for SX.
Therefore, we cannot determine the length of SU in this case.