Question

A parallelogram has sides with lengths of `14` and `15`. If the parallelogram's area is `42`, what is the length of its longest diagonal?

Answer 1

Length of the longest diagonal AC = 28.8533

Explanation:

Given `l = 15, w = 14, Area = 42`

Area of the parallelogram = l * h = 42
`:. BE = CF = h = (Area)/l = 42 / 15 = 2.8`

AE = DF = a = sqrt(w^2-h^2) = sqrt(14^2 - 2.8^2) = 13.7171#

AF = l + a = 15 + 13.7171 = 28.7171#

Longest diagonal AC `= sqrt(AF^2 + CF^2) = sqrt(28.7171^2 + 2.8^2) = 28.8533`