Question

A parallelogram has sides with lengths of `15` and `8`. If the parallelogram's area is `12`, what is the length of its longest diagonal?

Answer 1

Longest diagonal measures 22.9738

Explanation:

Given `l = 15, w = 8, Area = 12`

Area of the parallelogram = l * h = 12
`:. BE = CF = h = (Area)/l = 12 / 15 = 0.8`

AE = DF = a = sqrt(w^2-h^2) = sqrt(8^2 - 0.8^2) = 7.9599#

AF = l + a = 15 + 7.9599 = 22.9599#

Longest diagonal AC `= sqrt(AF^2 + CF^2) = sqrt(22.9599^2 + 0.8^2) = 22.9738`