the length of 2 diagonals of a quadrilateral is 10cm and 24cm respectively. both the diagonals are perpendicular bisector of each other. find the length of all sides of the quadrilateral and name it

Your quad must be a rhombus.

You will have 4 congruent right-angled triangles, each having sides 5 and 12
by Pythagoras the hypotenuse of that triangle is 13
(you have a 5-12-13 right-angled triangle)

so each side of the rhombus is 13 cm long