PQRS is a parallelogram. PT is perpendicular to TQR. PT=5cm,TQ=2cm and PS=10cm. Calculate the length of VR where V is where the diagonals intersect? ?

Given that PQRS is a parallelogram, we know that opposite sides are equal in length. Therefore, PS = QR = 10 cm.

Since PT is perpendicular to TQR, we can use Pythagoras theorem to find the length of TR:
TR^2 = TQ^2 + QR^2
TR^2 = 2^2 + 10^2
TR^2 = 4 + 100
TR^2 = 104
TR = √104
TR ≈ 10.2 cm

Since PT is perpendicular to TQR, we can also use Pythagoras theorem to find the length of PR:
PR^2 = PT^2 + TR^2
PR^2 = 5^2 + 10.2^2
PR^2 = 25 + 104.04
PR^2 = 129.04
PR = √129.04
PR ≈ 11.36 cm

Since PR is the diagonal of the parallelogram, it bisects the other diagonal QS at point V. Therefore, VR = 0.5 * QS
VR = 0.5 * 10
VR = 5 cm

Therefore, the length of VR is 5 cm.