Question

A parallelogram has sides with lengths of `14` and `15`. If the parallelogram's area is `70`, what is the length of its longest diagonal?

Answer 1

Length of the longest diagonal AC is 27.5967

Explanation:

Given `l = 15, w = 14, Area = 70`

Area of the parallelogram = l * h = 70
`:. BE = CF = h = (Area)/l = 70 / 15 = 4.6667`

AE = DF = a = sqrt(w^2-h^2) = sqrt(14^2 - 4.6667^2) = 13.1993#

AF = l + a = 14 + 13.1993 = 27.1993#

Longest diagonal AC `= sqrt(AF^2 + CF^2) = sqrt(27.1993^2 + 4.6667^2) = 27.5967`#