Question

A parallelogram has sides with lengths of `14` and `11`. If the parallelogram's area is `84`, what is the length of its longest diagonal?

Answer 1

Length of the longest diagonal AC = 24.6576

Explanation:

Given `l = 14, w = 11 Area = 84`

Area of the parallelogram = l * h = 84
`:. BE = CF = h = (Area)/l = 84 / 14 = 6`

AE = DF = a = sqrt(w^2-h^2) = sqrt(11^2 - 6^2) = 9.2195#

AF = l + a = 14 + 9.2195 = 23.9125#

Longest diagonal AC `= sqrt(AF^2 + CF^2) = sqrt(23.9125^2 + 6^2) = 24.6576`