Question

A parallelogram has sides with lengths of `15` and `12`. If the parallelogram's area is `66`, what is the length of its longest diagonal?

Answer 1

Length of the longest diagonal `AC = 26.509`

Explanation:

Given `l = 15, w = 12, Area = 66`

Area of the parallelogram = l * h = 66
`:. BE = CF = h = (Area)/l = 66 / 15 = 4.5`

AE = DF = a = sqrt(w^2-h^2) = sqrt(12^2 - 4.5^2) = 11.1243#

AF = l + a = 15 + 11.1243 = 26.1243#

Longest diagonal AC #= sqrt(AF^2 + CF^2) = sqrt(26.1243^2 + 4.5^2) = 26.509#