Question

A parallelogram has sides with lengths of `6` and `16`. If the parallelogram's area is `45`, what is the length of its longest diagonal?

Answer 1

Given `l = 16, w = 6, Area = 45`

Area of the parallelogram = l * h = 45
`:. BE = CF = h = (Area)/l = 45 / 16= 2.8185`

AE = DF = a = sqrt(w^2-h^2) = sqrt(6^2 - 2.8185^2) = 5.2968#

AF = l + a = 16 + 5.2968 = 21.2968#

Longest diagonal AC `= sqrt(AF^2 + CF^2) = sqrt(21.2968^2 + 2.8185^2) = 21.4825`