Question

A parallelogram has sides with lengths of `14` and `15`. If the parallelogram's area is `45`, what is the length of its longest diagonal?

Answer 1

Length of the longest diagonal is 28.8313

Explanation:

Given `l = 15, w = 14, Area = 45`

Area of the parallelogram = l * h = 45
`:. BE = CF = h = (Area)/l = 45 / 15 = 3`

AE = DF = a = sqrt(w^2-h^2) = sqrt(14^2 - 3^2) = 13.6748#

AF = l + a = 15 + 13.6748 = 28.6748#

Longest diagonal AC #= sqrt(AF^2 + CF^2) = sqrt(28.6748^2 + 3^2) = 28.8313#