Question

A parallelogram has sides with lengths of `16` and `15`. If the parallelogram's area is `16`, what is the length of its longest diagonal?

Answer 1

Length of the longest diagonal AC = 30.9827

Explanation:

Given `l = 16, w = 15, Area = 16`

Area of the parallelogram = l * h = 16
`:. BE = CF = h = (Area)/l = 16 / 16 = 1`

AE = DF = a = sqrt(w^2-h^2) = sqrt(15^2 - 1^2) = 14.9666#

AF = l + a = 16 + 14.9666 = 30.9666#

Longest diagonal AC `= sqrt(AF^2 + CF^2) = sqrt(30.9666^2 + 1^2) = 30.9827`