Question

A parallelogram has sides with lengths of `18` and `4`. If the parallelogram's area is `12`, what is the length of its longest diagonal?

Answer 1

Length of the longest diagonal AC = 21.9541

Explanation:

Given `l = 18, w = 4, Area = 12`

Area of the parallelogram = l * h = 12
`:. BE = CF = h = (Area)/l = 12 / 18 = 0.6667`

AE = DF = a = sqrt(w^2-h^2) = sqrt(4^2 - 0.6667^2) = 3.944#

AF = l + a = 18 + 3 .944= 21.944#

Longest diagonal AC `= sqrt(AF^2 + CF^2) = sqrt(21.944^2 + 0.6667^2) = 21.9541`