Question

A parallelogram has sides with lengths of `16` and `15`. If the parallelogram's area is `144`, what is the length of its longest diagonal?

Answer 1

Length of the longest diagonal AC `= 29.4109`

Explanation:

Given `l = 16, w = 15, Area = 144`

Area of the parallelogram = l * h = 144
`:. BE = CF = h = (Area)/l = 144 / 16 = 9`

AE = DF = a = sqrt(w^2-h^2) = sqrt(15^2 - 9^2) = 12#

AF = l + a = 16 + 12 = 28#

Longest diagonal AC #= sqrt(AF^2 + CF^2) = sqrt(28^2 + 9^2) = 29.4109#