The value of x is 7, and the length of RT is 109.
In a parallelogram, the diagonals bisect each other, which means that point U is the midpoint of both diagonals QT and RS.
Thus, QU and SU are equal halves of the diagonal QS:
QU = 4x + 9
SU = 3x + 16
Because QU and SU are equal halves of diagonal QS, we can equate them:
4x + 9 = 3x + 16
To find the value of x, we can solve this equation:
4x + 9 = 3x + 16
4x - 3x = 16 - 9
x = 7
Therefore, the value of x in the parallelogram QRST is 7.
The probable question may be:
QRST is a parallelogram. Find the value of x.
RT and QS are the diagonals of the parallelogram intersect each other at point U.
QU=4x+9, SU=3x+16, RQ=24, RS=37