Question

In a parallelogram a diagonal of the length 20 cm is perpendicular to one of the sides. Find the longer side of parallelogram if its perimeter is 80 cm.

Answer 1

If diagonals of a parallelogram are perpendicular to each other, this is a rhombus. A rhombus has all sides equal.
In the current scenario, the shorter rhombus is 20 cm long and has a perimeter of 80 cm

Side of rhombus = 80/4 = 20 cm
A quarter of rhombus is right angled triangle with hypotenuse being side of rhombus.
Half length of long diagonal = sqrt (20^2-10^2) = 17.32 cm
Length of longer rhombus = 17.32*2 = 34.64 cm