Question

A parallelogram has sides with lengths of `24` and `9`. If the parallelogram's area is `64`, what is the length of its longest diagonal?

Answer 1

Length of the longest diagonal AC = 33.7016

Explanation:

Given `l = 24, w = 9, Area = 64`

Area of the parallelogram = l * h = 64
`:. BE = CF = h = (Area)/l = 64 / 9 24= 2.6667`

AE = DF = a = sqrt(w^2-h^2) = sqrt(9^2 - 2.6667^2) = 8.5959#

AF = l + a = 24 + 8.5959 = 33.5959#

Longest diagonal AC #= sqrt(AF^2 + CF^2) = sqrt(33.5959^2 + 2.6667^2) = 33.7016#