Question

A parallelogram has sides with lengths of `14` and `12`. If the parallelogram's area is `28`, what is the length of its longest diagonal?

Answer 1

Longest diagonal measures 25.9095

Explanation:

Given `l = 14, w = 12, Area = 28`

Area of the parallelogram = l * h = 28
`:. BE = CF = h = (Area)/l = 28 / 14= 2`

AE = DF = a = sqrt(w^2-h^2) = sqrt(12^2 - 2^2) = 11.8322#

AF = l + a = 14 + 11.8322 = 25.8322#

Longest diagonal AC `= sqrt(AF^2 + CF^2) = sqrt(25.8322^2 + 2^2) = 25.9095`